I even bought a cheap $25 Behringer guitar compressor pedal to see what I was missing but it didn't help - later I realized that my guitar playing isn't repeatable enough. So this isn't the way to go.
What made it click was due to an accidental mistake in my normal workflow - I recorded some DAW-less techno jam stuff using GarageBand (normally I just copy the wavs from my little Tascam). While playing back, I noticed that there's a master compressor and I started fiddling with it. With repetitive music like Techno and House, the difference between no compression and full compression suddenly becomes very apparent (although still somewhat subtle compared to other FX commonly used in music production). Also it helped that my recording had no compression on it - comprising just a raw drum machine and mono-synth.
IME, you can get a feel for what the threshold and ratio are doing pretty quickly, and that's probably enough to be useful. In broad strokes that's all you need to make them "work". If you have the attack set way fast, you'll start to hear the signal get a bit muddy.
But attack and release (especially on a lot of plugins) are a bit funky, and I still can't tell what the knee is doing unless I move the knob around. And I own a couple clones (76kt or gold comp 2a) and a couple of distressors, and they sound different but I still need play around with them to coax them into what I think they should sound like.
My advice for learning is to totally overdo the compression on a drum track (snare, kick, hats, etc) and play with the settings. Ideally these drums are uncompressed.
Using a 4:1 ratio, lower your threshold all the way down until you're getting > 10 dB of gain reduction and then start playing with the attack time. What do you hear when the attack time is at 0 ms? What do you hear when you start to slow the attack time? 5 ms? 10 ms? 30 ms? 100 ms?
Then do the same with your release time. Start with it set as fast as it will go and then start to slow it down. What do you hear happening?
Once you have the attack time and release time feeling good then raise your threshold so that the compression is less heavy-handed (unless you like it). Set the threshold where the level of compression feels good to you.