I'm not 100% sure what you mean by compressor "tone", but if you mean frequency modifications, then this ain't the normal role for a compressor, that's the role of an equalizer (unless it's a multiband compressor, which is essentially multiple parallel compressors operating independently in different frequency regions).
Regarding compressors, I could give you some quick starters (I remember it took me some time to understand it). Compressors are *very* versatile tools, and the theory is actually simple; the idea is to dynamically reduce volume peaks in the audio, often in order to be able to (AFTER the compression) increase the overall volume of the audio without reaching the clip limit (sometimes called gain-riding, peak limiting, maximizing intensity or whatever people call it). It is somewhat like first "averaging" the audio with a compressor, simply put, and then raise the overall volume after the compression. And what about all those knobs? Well, it's easy too:
"Threshold" is at which particular volume the audio will be reduced in volume (audio below the threshold will be unaffected).
"Ratio" is how much the audio will be reduced.
"Attack" is how fast the compressor will react to peaks and start to work.
"Release" is how fast the compressor will release and return to the unaffected volume level.
"Knee" is how the region around the threshold looks like; often hard or soft, "hard" being "linear" volume change, and soft being "exponential", "smooth" volume change.
Simple, eh? Well, sorry to say, what's not easy is how to master the technique. As users have said above, I have to agree with them: the only thing to do is to try it for yourself, and try it with different types of audio. Experiment and experience is the key here, sadly. Compression can and *will* sound very differently depending on compressor type, settings and the audio being processed.
Nevertheless here are some starting points for you (settings propositions which I've collected from various sources, god knows where, and sorry for the shitty format, but here you go):
SOURCE|ATTACK|RELEASE|RATIO|KNEE|GAIN REDUCTION
Vocal (normal) 25-100 ms 100-500ms/Auto 2:1-8:1 Soft 3-8dB
Vocal (rock) 25-100 ms 100-300ms 4:1-10:1 Hard 5-15dB
Acoustic guitar 5-10ms/100-500 ms 100-500ms/Auto 4-10:1 Medium 5-12dB
Electric guitar 2-5ms 500ms/Auto 8:1 Hard 5-15dB
Elec. guitar (raging) 25 ms 1-2 sec 4-8:1 Hard 5-15dB
Drums (Kick & snare) 1-25ms 25-200ms/Auto 4-10:1 Hard 5-15 dB
Drums (Cymbals) 25 ms 1-2 sec 2-10:1 Hard 5-15 dB
Bass 2-10ms 500ms/Auto 4-12:1 Hard 5-15dB
Bass (Clicky) 25 ms 25 ms 4-12:1 Hard 5-15dB
Bass (Mushy) 100-500 ms 100-500 ms 4:1 Hard 5-15dB
Brass (Horns) 1-25ms 25-300ms/Auto 5-15:1 Hard 8-15dB
Mixes Fast 400ms/Auto 2-6:1 Soft 2-10dB(Stereo Link On)
General Fast 500ms/Auto 5:1 Soft 10dB
Very low frequencies (below 20 Hz) present in a soundfile should be removed before compression; this makes it easier to monitor audible frequencies while compressing.
I'd say, when used correctly, compression can almost always be used to improve audio. Particularly vocals, which almost always needs compression. And things which might have been recklessly played (tough guitar or bass tracks, where certain tones are unintentionally less loud than others). Background sounds and pads also very often gain (no pun intended) from compression. And weak drums (particularly bass drums, snares and toms) can be (and very often are) compressed in order to get that *twang* out of them.
You can use a compressor when recording (i.e. recording with an external compressor connected) if you are afraid of peak clipping during the recording.
This is often the case with vocals, which generally has a very dynamic range. But, you can also use software compressors after you've recorded; there are quite a few very good ones out there. Personally, I almost always compress anything and everything, but that's me

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And last - but certainly not least - compression on the entire final stereo mix (the mastering process) is a very, VERY common method to reduce the dynamic range in order to be able to increase the overall final loudness of a track, sometimes called the "loudness war" for radio stations. But final mastering, that's another story, and not told here...
Here's a good starting guide with a couple of chapters on dynamic processors (incl. compressors) and even a pdf:
www-dot-rane-dot-com/note155-dot-html
(replace dots with "."; this forum does not allow me yet to add full url:s)
Well, this reply is starting to look like a seminar, so that's it for now. Can't use any audio compressor on this reply

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Regards, and good luck compressing!
/DeNilson