Now with digital everything these days, it's actually even easier. Some of these compression plugins have so many meters and controls that were missing in the old hardware days, that you kind of can't screw it up. Not to mention the ever popular failsafe called "presets".
The first thing I want to get to is explaining what some of the common functions are in compression tools.
Threshold: The threshold is your desired audio level. The more you turn it down, the more the plugin will compress in an effort to reduce the level of the audio to your chosen level/Threshold
Knee: This is how abrupt the transition will be between no compression and when it kicks in. A "hard knee" will be abrupt while a "soft knee" will be more subtle.
Attack: This will define how quickly the plugin reacts when the incoming audio raises above the chosen threshold level.
Release: Release sets how quickly the compression will fade off after it is triggered.
Makeup: Not the kind you wear on your face if you are in an 80's metal tribute, but the kind that brings the output level back up after the compression has brought it down.
Using compression on different types of instruments.
In the video below I show my personal technique for compression on a snare drum, a vocal, a bass guitar and a piano track. Just watching this video should give you a much better idea on how to use compression if you currently have no idea what you are doing.
Using compression on Sub-mixes and Mastering
An awesome multi-band mastering compressor is a must when mastering audio. In fact, it's the only thing I put on a master track other than a frequency analyzer to visualize where my levels are. Using a good compressor on a drum sub or vocal sub is also a must in my book.
The purpose of using a compressor on these types of tracks is slightly different from what we've learned above for individual instruments in that you are now using it to raise the levels and intensity while forcing the audio not to exceed the threshold. Aka "Punch".
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For mastering I use either the FabFilter Pro-MB or Yamaha's Final Master. Both are multiband compressors and both do an equally great job. The FabFilter is a bit more comprehensive though. You would use the multiband functionality to compress or intensify at different levels, each band.
Here's a video showing my technique for submix and mastering with Multiband compressors.
I hope I've helped you to understand compression a little better than you did when you started reading this. Load a small project and mess with compression plugins until you get a feel for what controls do what. Happy squashing!