Hey there guys,
Ive just finished my 3 year uni course doing music technology so thought i could shed some light here.
There 2 ways to do it really.
You can either connect your mics via xlr cables to a external mixer (something like 8 channels) apply eq and set levels here then bounce to a stereo track into your computer.
The best way IMO, get a firewire/Usb audio interface. As Luke meantioned, the presonus products are great. I personally use the FP10 by presonus. its about 300 GBP (last time i checked)
This basically gives your 8 XLR inputs which is enough for a 5 piece drum kit+overheads. It also has phantom power for all 8 channels which means you can use condersor microphones (which is a must for overhead mics).
The firewire interface itself will allow you to record 8 seperate channels and the FP10 comes with cubase for windows and mac which is a great DAW (digital audio workstation) to start with.
It will allow you to add effects, change levels, send to busses and finally bounce down on to a stereo track.
Heres a picture of the interface.
I hope i was some help!
Check my youtube channel
to hear the drum sounds if you want. Using red5audio mics. They are low budget but are pretty good quality.