Ok, i dunno how much background you have with this stuff, so if it sounds like i'm mickymousing you along, don't get mad at me. I'm just trying to cover everything.

I'm also going to try to not do this specific to your gear, that way it's aplicable to anything you might come across.

The way I get certain "sounds" for various things when playing or mixing live or mixing a recorded song is, i think of the sound i want to hear out of what's there and i do it. Simple as that. (usually.)

The way to get to that point is to
1)know what the knobs are actually doing to the signal
2)understand how that change in signal relates to the change in audible sound
3)know what characteristics of the voice/your instrument come through which parts of the audible spectrum

The first one can be easily learned simply by reading and understanding. the Second can be mostly learned the same way. While you still do the same and "leanr" the third, actually understanding how the first two interact with the third is something that comes over time through trial and error, and having your ears get used to pulling out different things and identifying frequencies in the air (like hearing a bit of feedback and knowing that it's at 400Hz, or 900Hz, or 6KHz without having to reference the pitch to anything or search for it on the eq)

You seemed to have a solid grasp of the mechanics of the EQ already, but i'll get into it a little so that it's covered and i know i have a reference point for anything that might need to be applied.

Basically, an EQ is a +/- gain knob for sepearte/specific chunks of frequencies. At unity, that frequency range is left unaltered. Obviously turn it towards the - and you reduce that freqency's volume, + raises it.

Knowing what kind of EQ you're working with will also give you an idea of how you're going to attack this too.

Basically there are
Graphic EQs: they're the ones with a long line of faders that go up and down, and look like a graph, or an actual graphic representation of what the boosts and cuts will look like along the spectrum. It looks like the Fishman re/DI you have has a small graphic.

Parametric: These can be as simple as Bass & Treble boost/cut, or can have several parameters to adjust, usually in knob form. These are on most mixer channels and and guitar amps (and active guitars) have these types.

Then there's Para-graphic which is a combination of the two and less common.

On a parametric you may find any combination of these:

Low Shelf The low shelf takes the signal from a certain frequency and boosts/cuts everything below that evenly, creating a "shelf". Some have a seperate knob where you can pick the frequency at which the shelving begins, others are fixed and you can just control the +/-gain.

Low Cut/High Pass They're different names for the same thing. Instead of creating a shelf, these just start rolling off the signal at a certain point until you're at negative infinity dB. Most of the time on cheaper gear it's just a button that cuts off starting at around 60Hz or 80Hz. It's either on or off. More complex filters, you can control how quickly it rolls off, the frequency it rolls off at, is it a hard knee or soft knee, linear rolloff or parabolic (rounded) rolloff...etc.

There's also (usually) then a High Shelf and (rarely on EQs, often on synths and samplers) a high cut.

Other than shelves and cuts are regular EQs, usually labled as Mid EQ, but can be named almost anything. These look like bell curves (like the ones nerds used to ruin in school) on the auditory spectrum

Simple EQ will have just a Mid +/-Gain at a fixed frequency with a fixed bandwidth. More powerfull Mid EQs include knobs for:
Frequency; simple enough, you can select what frequency you want to boost/cut.
Q: Q is used to represent Bandwidth, or how wide of an EQ you're going to do. (if you know all this alreayd, i'm sorry) Often you can adjust the width of the Q to manipulate as wide as 3 octaves of signal, all the way down to only 1/12 of an octave of signal (or rather, 1/12 of an octave would be 1 specific individual note)

Knowing the differences between those different EQs helps know that boosting a Low Shelf 3dB @ 100Hz will affect the sound differently than boosting a regular EQ 3dB @ 100Hz. The difference in this case might be slight, but the slightest shit makes a big difference with EQ.

That pretty much covers #1, what the knobs do to the signal.

How does this relate to the changes in the actual sound? well, i'll start with the bandwidth.(this all works for both live and recording, same principles at work here)

Let's say you have your guitar recorded and you're listening and it gets really muddy and cluttered around oh, 450Hz. You'll know that you have to set the frequency to 450Hz and then lower the gain. But, you can lower the gain to -15dB @ 450Hz and it can still be muddy, just muddy with a really narrow chunch of signal cut out of it AT 450Hz. So you have to look at what makes things muddy, or hard to hear, or cluttered. Anything that sounds like it's fighting for sonic real estate, probably is doing just that. Fighting for space. There's too much sonic information there for something in the signal path to handled. Tones start piling up at and around that frequency and there's no room for it all. Knowing this, you widen that Q to cover everything from 300Hz to about 550Hz say, and only cut the gain as little as -1 or -2dB, it will really start to breath.

On the other hand, lets say you have a drum track recorded and every time a certain tom is hit, there's this godawful ring that resonates over the whole mix. You know what the problems is, it's an isolated problem, and is probably only happening over a very small segment of the sonic spectrum. Ideally you'd have the idiot drummer tune his kit so it stops ringing out, but this works for a lot of things that have this problem, its a good example, and sometimes you're stuck with a bad drummer/drum kit/recording/etc. But you know what the problem is, and once you find where on the spectrum it is, you set the Q so it's wide enough to mask the whole problem area, but narrow enough that it doesnt overreach itself and start altering sound you don't want altered. Then you cut it -3, maybe -6dB, maybe more if you need, and viola, terrible drum artifact is gone without compromising all the good sonic information in the track.

A great way to find a trouble spot is reversing that...Set the Q to a moderately tigh 3/12s of an ovtave or so. Not too too narrow because you might miss what you're looking for. Then boost the gain unnaturally high. Not to high because it will start clipping and you wont be able to hear what you're looking for, and it will all sound like shit. Then sweep the frequency knob slowly until it juices up the really bad spot. You can't miss it. It will sound soooo fucking bad. Leave it at that frequency and then cut the gain to the - side of U and maybe widen the Q just a touch to make sure you got it all. Tada, no more terribl sound screwin up your mix.

The same applies to boosting. Wide Q will give you a nice round boost, while a narrow Q, especially one boosted too many dB will create an unnatural sounding peculiarity of sound because it emphasises too little of the sonic information. Also, the more you boost or cut the frequency, the narrower the Q gets with respect to the amplitude of the boost/cut. A really narrow Q boosted only 1dB reacts more naturally than a towering 10dB boost at 1/12th an octave. The bell curve gets skinnier and taller at the same Q. You can also use a similar method to find the really sweet spot by boosting and sweeping till you find the sweet spot, and then lowering the boost, but still keeping to a comfy level in the +, widen the Q and lower the overall track. now the sweetspot of that instrument will stand out

Now that you know (already knew) this, the next step is to read up on the Overtone Series. This is super important to being able to understand how to get a sound and EQ without much trial and error. Without getting too far into it. . .Play a A note on your low E string. You're playing A (i beleive that one is a 220hz, it could be something esle) But inside that waveshaped the string makes while vibrating, it's also making other notes starting with the Octave, than the 5th above the ovtave, and so on in more detail than i'm describing. That's the Overtone Series. All those other notes are in that 1 note you're playing, and they're all playing at different intensities. Different instruments' Overtone Series have different characteristics based on how strong each of those Overtones in that note is. That (plus the actual waveshape the instrument creates. . .the natural deformities of a "pure" sine wave that are unique to each instrument) are what create tone.

That means knowing how the overtone series for your instrument and voice work help you know exactly where to EQ. you know your guitar only goes down to your low E string's lowest note, E (barring any downtuning) Other than banging on your guitar, there isnt going to be much "useable" musical information below that point, so you can cut it if you so choose, it helps reduce noise and leaves room for other sonic info. lets say you want to bring out the lowest notes on your guitar, they're for some reason not coming through in the mix, but if you boost the frequencies of those notes on your amp (boost the lows) things get muddy and then start competing with the bass. Knowing the overtone series lets you know what other notes are actually in those low notes. You know you can boost a wide Q a whole octave above the notes you're playing, and you're actually boosting not the fundamental frequency of that note, but the first and second partial in the overtone series. And without actually boosting your lows, without boosting the notes you're playing, you've boosted the notes you're playing, all without making a sonic mess.

Also, a lot of times if you have to EQ out a bad spot, you're also EQing out some important musical info. Knowing the Overtone series will help you make up for what you've taken out bring it back by boosting the first partials.

That's the basics of #2 without writing a text book. Once you've got a graps of #2, you now have the daunting task of applying it to # 3, and then being able to know what to do without trial and error . . .which is inevitable, because the only way to really do that is through repetition, trial and error, and training your ears. The difference being that trail and error used to belay with the knobs till it sounds right. Now it's: When i do this very specific thing, i hear how the sound reacts and see why my adjustment made it sound that way. Over time you'll get it.

One way to speed up the process and at the same time understand the characteristics of the sounds your guitar/amp/gear make is to plug in. Put all the EQs on your amp/DI at unity (flat, no boost or cut). For this process i'd probably pretend like the DI doesnt exist and focus only on your amp's settings. Play around with the gain knob noticing how the signal "reacts" to the gain stage. Look at the differences in tone between playing with the gain down and the gain up. Do certain frequencies seem to get louder more than other frequencies? If you have a Gain and Volume, do this with a low volume and a high volume. Ideally, gain stages should be transparent and raise all frequencies equally so that the entire flat line of the spectrum gets amplified evenly. . . but that's magical fantasy amp land. Different methods of building amps, different circuits and different components elicit different reactions from the signal, and that alters your "sound".

Now that you've familiarized yourself with the affects of the gain/volume with everything flat, start with the EQ. (i'm gonna pretend your amp has the basic Bass Mid Treble knobs. If there's a low mid and High mid, or if there are more knobs that we've gone over, adjust acordingly.

This isnt so much to hear what the EQ is doing, but to hear the different parts of sound your guitar makes. . .and then from that what the EQ is doing to it. I'd suggest doing this systematically, but some people dont work that way... Starting with the bass (hopefully the amp's manual says what kind of EQ you're working with, but it's not too important for this) Cut it out completely and play around various different techniques and styles. Play all over your neck. Notice what tones your guitar is creating. It's your guitar creating the tones. (think back to the overtone series) Your amp is just making them louder. The EQ on your amp is really just altering different parts of notes. Cut the bass and play a low G and you still hear sound because that note is making higher pitched information at the same time. Now with your bass still cut, cut the mids also, leaving only the highs at Unity/Flat. Continue playing. Familiarize with the sounds and tones your guitar creates all over the neck that is in the High EQ's range; that the Highs "let through". Then cut the Bass and High, and leave the Mids up. Play. Just as with the highs Notice what pitches and tones your guitar creates (not just notes, but pick rakes and finger-on-string motion, etc. for bass mid and high.) that the MIDs "let through". Again for the Lows. It's tough sometimes because you almost have to think about it in a super sterile textbooky, non-musial sort of way. But once you understand it that way, it makes everything easier. Just remember to think about it in terms of Sound your guitar makes, that the EQ lets through, not what has this EQ done to my sound.

Now that you've heard what each knob is in control of, zero the amp (put all them EQs back to Flat/Unity.) Play a chord or two, maybe play a scale up and down once, just to reset your ears. Then pick a sound you want to emulate. Think of a specific song with a distinct guitar tone (don't cheat and pick one who's setting you've memorized). Then put your guitar down. Go over to your amp sans guitar and remembering what tonal characteristics were 'let through' each EQ band. Think of that guitar sound you want, and then put those EQ knobs in the positions that would represent the amounts of each of those guitar sounds you need, to get that tone. Make sense? I hope. Whew. Now pick up your guitar and see how close it sounds to what you wanted. Tweek until it's "just right/good enough" and then see how close your initial Blind settings were to what you really needed. Maybe you got it close enough the first try...if that's the case i'm going to consider a career teaching audio engineering. If you didn't get it anywhere close, it's just a matter of time before your ears and textbook-understandings align and you can just think about it, and make any amp sound like you want without trial and error. (Of course every guitar, pickup, and amp have their "own" sound as well. If you really wanna get into it, you can add Strings to the list, and pick type, and the room and even the cables you use have their "own" sound. But that's another story altogether.)

There are also references out there that i'm sure googling for a while and you'll find them. . . .they'l go over what happens at what frequencies. Mud happens in this frequency range. Gs and Ks and Ds (gutterals) are pronounced at that frequency. Esses and other Cybalants come through at certain frequencies. When you sing, all the different cavities in your body act as resonators, and they're all different sizes, so they resonate at different frequencies. If you think you sing too nasaly, a touch of the right EQ in the right frequency range will hide that. Throat sounds come in at a different frequency. There's so much of that information to know and there's so much out there about it, i'm not gonna get into it either. But if you know what happens in what frequency ranges, you can EQ your voice without the guesswork too. You just hear what's wrong and what's right, and you know right where they are.

Since i do sound i try to stay away from the PA/Sound system unless i'm gettig paid, because, well, i don't wanna start doing shit for free that i should be getting paid for. But sometimes when i'm out and there's a feedback problem and i see the poor bastard who doesnt know a thing about sound buggin out trying ever (wrong) thing to get rid of the feedback, i'll go over and tell him exactly what frequency to cut on the PA or Monitor's EQ. I don't have to play with the EQ to find the frequency. I don't have to reference that frequency to anything. I just hear it, and know, that sound is right about at that certain frequency; it has it's own character. I'm not magic, it's just something that came from doing live sound and killing feedback on a weekly basis. Your ear/brain get pitch-memory. (ahem overtone series) that has everything to do with being able to know how to get the sound you're looking for without playing around for 20 minutes every song.