You'll need alot of gear and most of the quality will depend on your budget. I didn't mention any prices, as i live in Belgium and it looks like everything is twice as expensive here.
Mics
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Let's say you need 4 tracks for your drums.
So you'll need 4 mics. 2 mics for close micing (kick and snare are most important) and 2 mics to get the drumset 'alive', to catch the cymbals, hats, toms and the room, called: Overheads.
Snare:
Shure sm57 is a very nice starter mike that you'll probably wanna keep for the rest off your life. It's quite popular. Other options are senheiser md421 or md441 (better but more expensive!) The E60.. (with the drummountclip thing on it) sounds nice aswell. Put it on the top head (batter) about one inch above the rim, pointing at the middle (listen to the sound while you're placing it).
Kick:
Akg D112 is pretty much a standard, i love it some love others ... like md 421, audixd6 , e602, EV re20, .... place it inside the kick pointing at the batter, try outside aswell.
Overhead:
You'll need 2 (matching) condesor mics mostly prefered small diaphragm, like rode nt5, SP c4, mxl 603, shure sm81,
akg c 451, ...
A large diaphragm mike, like SP b1, akg c 414, ... can do wonders aswell
Mess around with stereo mic techniques, like xy, spaced, ortf, ...
Preamps:
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You'll need preamps to preamplify your mic outputs. You can either use stand alone preamps, ore mixers, with built in preamps.
You have four mikes, so you'll need 4 preamps, or 2 dual preamps. Possible suggestions are: m-audio audiobuddy or dmp3, RNP, .... Make sure they have phantom power, or you get another device that provides phantom power.
If you wanna use a mixer, you have the advantage of using more mikes (for toms), submix them with your OH's to a stereo track. A 4 bus mixer would be handy, otherwise you can use the inserts as outputs. Some suggestions are behringer (if you're on a very low budget), mackie, soundcraft, ...
Soundcard:
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So you've got your sound on decent levels, now you have to record it. You'll need a soundcard with analog inputs: Like m-audio delta 44, digi00blahblahblah or terratec ews 88, .....
Software:
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Some soundcards have software with'm. If it doesn't, you could use cubase, nuendo, cakewalk sonar, adobe audition (love it), .... These programs mostly have some plugins (for compression, reverb, eq, ....). Other options are waves plugins or some free plugins that you might find on the web.
As you see there's a long way to go to make descent recordings and you could have saved me from typing all this if you read alot on this site. There's a million books of information here on the bbs, especially harvey's big sticky thread in the mic forum, go check that out !!!
hope it helps though
greetz, fazil