I'm not by any stretch of the means an expert on this, but I am aware of what at least most of the controls are capable of, so I'll try to explain it.
The ratio is the rate by which the signal gets compressed. For example, if the ratio is 2:1, that means that for ever dB that the signal goes over the threshold, it is reduced by 2 dB.
The attack is how fast the compressor kicks in, and the release is how long it takes the compressor to "let go of the signal"
The threshold is similar to setting the peak or level that the signal has to hit before the compressor is activated, so if you set the threshold to -10 dB, whenever the signal hit that or passed it, the compressor would kick in.
Now, the signal will seems quieter when it's compressed, so that's what the make-up gain meter is for, as you slowly bring that up to get the signal back to a comfortable volume.