It has become part of recording folklore that you should compress the snare and kick drum. But first, you have to know why you are doing it. If you do not know why, then you're never going to get a good result - the sound you achieve will be no more than the work of random chance.
Compressing individual drums vs. the whole drum set
There are two ways you can approach compressing the drum set. One would be to compress individual drums, the other is to compress the drum set as a whole. These will produce entirely different results. You can do both if you wish, but here we shall concentrate on compressing individual drums, principally the snare and kick, but also the toms too.
The sound of drums without compression
A while ago an experiment was carried out where a snare drum was recorded and the recording played back through a PA system. The sound of both the drum itself and the PA were fed to an audio analyzer. Apparently, to reproduce the sound of the drum accurately and maintain the transient (the initial strike) properly, it took 1000 watts of amplifier power.
The reason for this is that the transient, the very first few milliseconds, is VERY loud. The sound dies away quickly after that. So to reproduce the transient accurately, a lot of power is needed. In recording, then the level must be set so that the transient does not exceed 0 dBFS - the full scale level of the system before the red light comes on.
Why drums need compression
The problem now is that the transient is much louder than the 'body' of the sound, as the strike dies away. But the transient is short and does not fully register with the ear. So the drum is actually a lot louder than it sounds. Yes a drum played live sounds loud, but any other instrument played continuously at the level of the peak of the transient would be truly ear-splitting.
If the transient therefore can be made quieter than the body of the sound, overall the strike will sound subjectively louder. Actually, 'louder' is probably not quite the right word for the subjective experience. 'Fuller' or 'more powerful' would be better.
How to set the compressor to make the snare and kick sound fuller and more powerful
Every compressor - every decent one - has a control labeled 'attack'. This is confusing. Anyone new to compressors would think that more attack means a more attacking sound. In fact this control sets the speed at which the compressor responds to a sound. If you set a long attack time, say 100 milliseconds (a tenth of a second), then the transient of the drum would get through before the compressor had time to respond. So to lower the level of the transient, you should set a very short attack time, as low perhaps as just one millisecond.
When compressing individual drums, the attack time is the most important control. The compression ratio can be set to around 4:1 and the release time to 100 milliseconds. Naturally you should experiment with all of these settings.
Problems with a short attack time
One thing is very much for sure, you have to experiment with the attack time. Setting an attack time that is too short will result in a 'flattening' of the sound of the drum. It just doesn't sound natural any more. So you should pay a lot of attention to very small movements of the attack control because these small movements will make a lot of difference.
Differences between the snare drum and the kick drum
The main difference between the snaredrum and the kick drum is that the snare is always a very attacking sound with a sharp transient. The kick is always less attacking, but the degree of attack can vary. If a hard beater is used, then the sound will be attacking. Sometimes a piece of hard plastic is attached to the drum head to emphasize this. But if a soft beater is used, then the sound will not have such an aggressive transient. Either way, the sound can still benefit from compression. But you have to use your ears and fine-tune the settings to get the best results.
Compressing the toms
Toms can also benefit from this type of compression. However the body of the tom sound is louder compared to the transient than in the snare and kick drums. So effectively, the sound is already compressed in comparison to the snare and kick. Therefore, although this style of compression is certainly applicable, generally less compression will be used than for the snare and kick.
Summary and further considerations
What we have learned here is how to reduce the level of the transient compared to the body of the drum sound to make the overall effect fuller and subjectively louder. There are occasions, not covered here, where you might want to emphasize the transient. There is also a significant difference, not covered here, in the way you would approach compression of drums in digital and in analog recording.
Great home recording starts with a great home recording studio. It doesn't need to be expensive if you know how to select the right equipment for your needs.