It's a simple four-step program...
 
1. Find out what compressors your favorite record producer is being paid to endorse, and buy them.
2. Find out which compressors faithfully emulate the hardware your favorite producers of years gone by used, and buy them.
3. Post on KVR "what's the best compressor?", write down the 150 recommendations you'll get and buy them all.
4. Use every preset and struggle quietly as you try to figure out which one will reveal the promised pixie dust.
 
5. (Optional) Study what compressors actually do so you know what to listen for, then go back to KVR and sell all your compressors to the next batch of frustrated seekers.
 
Seriously, though, compression has basically two uses: envelope shaping and leveling. Every application is some variation on those two things. Start with the simplest, bus glue. It's a form of leveling, wherein the loudest moments are quieted and the quiet moments are made louder. And despite internet lore to the contrary, you can do it with nearly any compressor.
 
The main variables are attack and release times, which determine how aggressive the effect is going to be. Do lots of A/B comparisons as you experiment with these parameters. Use large ratios (8:1 or higher) to start with, so it's easier to hear what's happening, and then gradually back the ratios down to gentler values (2:1 or less).
 
When dipping your toe into the multi-band world, start with just two bands crossed over at ~200 Hz and note how it differs from a broadband compressor, not just in the low frequencies but also in the high end. Listen to high-frequency percussive components such as tambourines, shakers and ride bells. Note that they remain more distinct as you turn the volume up when lows are compressed independently of highs.

I agree with the approach Mike Stavrou does. Here is basically what it is. I have posted this before. I find it really works.
 
How to set up a Compressor (properly)
 
A good tip to get a robust good quality sound out of a compressor is setting the parameters of a compressor in the right order otherwise you will never get it right. You need it to do a certain job and want the signal to still maintain a higher integrity. Putting it the other way a compressor can also make your signal sound bad.
I got improved results by doing it this way. If you do this you will get much better sounding compression on your tracks or mix busses. Think ARRT. Attack first, then release then ratio then threshold last. Here is how you do it. This works equally well on individual sources as well as busses and final mixes.

Lets set Attack first.

Start by setting the ratio very high, release as fast as it will go. Now feed audio in and lower the threshold until the compressor starts kicking in and you can hear it. Listen to the attack part of the music. The leading edge or attack transient. While the Attack setting is fast the compressor will jump all over the music and literally destroy the front edge of the sound. Slow the attack down slowly so the desired attack transient is achieved. Listen to how even as you start to apply small amounts of attack the music or the transients all come back and start to sound good again.

(Note: People often have the attack setting too fast and the compressor is destroying the attack part of the music. No matter what you do with other parameters the music will always be screwed) Setting the attack is very important for final mixes as well. Too fast and once again the music is destroyed. The ultra fast release lets you hear far more individual attacks than a slower setting.

Now we set Release

Release controls the speed at which the sound glides back after you have punched it away. The idea is to get that speed to become a musical component of the sound. Think how slow can I get it while maintaining some control. The power in a groove is in a slower moving wave. Listen to Release and feel the way it bounces back at you and at some point it will be like a swing.  This time does not necessarily have to relate to quarter notes or the groove in the music so much but an overall release groove.


Next we set Ratio

The idea is to lower the threshold as much as you can without losing the effects you have created with Attack and Release. The higher the ratio, the smaller the sound is, although it is more controlled. The lower the ratio as in 2:1 it feels like a larger image. The idea is to find a ratio that sounds big but is controlled. Listen to the size and firmness of the sound.

Last we set Threshold

It is desirable to set the threshold so that the compressor is not compressing all the time (Unless that is the effect you want of course) The correct setting will see the dynamic movement coming to rest at special moments. Too low a threshold creates a flat lifeless sound. Permitting the dynamic movement of the sound to come to rest in some quieter moments allows that moment to attain a momentary bigger 1:1 presence and prevents it from rushing towards the listener with unwanted noise. It is bad enough that quiet moments are small without being squashed smaller still due to higher compression ratios. Each time a sound comes up for air it attains a sense of reality a 1:1 ratio.

Makeup gain or output level

Compressors by their very nature are attenuating the signal so the output needs to be put back to where the input signal level was originally. Use the gain reduction indicator to give you some idea. ie if a compressor is providing mainly - 3db of gain reduction for half the time then set the Makeup gain to +3db to get the signal level back up to where it was.

Compressors are not black art or require rocket science. They are simply one of those processors you need to be careful with and have an approach to setting. Using this method above will give you great transparent sounding results. Even cheaper compressors will sound better after doing it this way. And even if you adjust them differently to this method, try it and see how it sounds after. You might be surprised.  One of the problems is that you cannot setup a compressor fast and move on like you can with other effects. The compressor takes time to get it sounding right. The moment you insert one you have to be prepared to put the time in to get it right. Don't rush it!
 
 
 

As Jeff says, attack is usually the most critical setting and often the best place to start. I think one of the reasons people struggle with attack settings is they don't have a practical mental image of what different lengths of time sound like.
 
For example, say you want to allow the initial crack of a snare through...just how long does that attack need to be? Is 10ms too long or too short? How about a bass drum? Or a vocal consonant? How much longer is an "S" versus a "T"? The pluck of a fingered bass versus that of a picked bass?
 
To get to the point where you just know where to start with attack (and release) times, you have to first be able to mentally correlate audio events to units of time. The quickest way to learn that is to zoom in on transients in your DAW and let the timeline tell you how long they last. You might be surprised to find that many events are much shorter in duration than you think, and that you've been unwittingly setting your attack times too high.