You will notice the difference most easily with transients. Try this:
Figure out some way to get loops of a few very simple sounds. Audacity, Hydrogen, whatever. Free software is available to do this if you do not already have something working. Start with a snare drum, quarter notes at like 80 bpm or so. crack ... crack ... crack ... etc. If you don't have the means to patch a computer in to the system you are using burn it on to a CD and bring that with you.
Turn the ratio up pretty high, higher than you would ever actually use on a snare. We are not looking for something pretty, we just want to hear the results of different attack times. Start with the attack as long as it will go. On a sound like a snare you will probably not be hearing anything, by the time the compressor has clamped down the sound is over. Now start moving the time down in small increments, comparing the bypassed to compressed sound. As you start seeing some gain reduction happening compensate with the same amount of makeup gain. At first the initial attack will still be unaffected but you will start to hear more sustain in the body of the drum. That's a slower attack time letting the initial transient through and then clamping down on the body. Eventually you will get to a point where you hear a marked difference in the sound of the initial crack. At that point you are using an attack fast enough to clamp down on the initial transient.
Try the same thing with a kick drum. With a low pitched source and a fast enough attack you can eventually get to the point where you start hearing distortion as the compressor clamps down on each cycle of the wave. Listen for that.
That's just a couple things to get you started. Again, the key is listening. Mix with your ears, not your eyes.
