Hi jwh,
It took me a while to hear it as well...in fact, as with most things, I'm still a work in progress, but I do have a bunch of compressors, both hardware and software, and I can try to explain what my process is like.
When I listen for compression I listen for essentially three things:
1. Listen to the spaces. Listen to the material for the empty spots and then listen to what happens to those spots when compresson is engaged. When folks talk about "glue", what they mean is how sound fills in the spaces in the music. I sort of set a mental baseline for the level of the peaks in the music, (for me it's usally snare drum), then apply compression and makeup gain until those peaks are the same with the compressor engaged and with it bypassed. Use your meters to make sure that you have a good A/B test, then listen to what happens to the space around the peaks when compression is engaged.
2. Listen to transients. Another good way to think about compression is how it can minimize transients (specifically with a fast attack time). Again listen to snare drum...normally you'd hear a loud-ish initial transient followed by a fairly fast drop off in signal. Compression can squash that transient so that it's not louder than the following signal. Listen to Eric Church's "Creepin" for a good example of this in a snare drum (even if, like me, you don't much like country/western). The snare in that song is really squashed. It's compressed so that it almost sounds like a burst of static at a constant volume.
3. Listen to compression as though it were an EQ with saturation. Compressors impart a "sound", almost like an EQ with saturation (that's not quite right, but writing about sound is always a bit imprecise). A good way to see one possible example of what compressors do is by passing a sine wave through a tube compressor, applying compression and comparing the wet and dry signal in a spectrum analyzer.
Next, A/B with different compressors. Use sends and busses with different comps on them to switch back and forth. Repeat. Repeat. Repeat. Repeat again till you figure out that my descriptions are wildly off base and that the sound of compressors can only be described in terms that you understand. Explain it to someone else. Have them tell you you're wildly off base and then realize that both of you are correct :)
Good luck
Dean