sh0rd87, don't get mad... get'xited and start recording

. You've got drums, you've got mics, you've got mixer, you've got recorder (your computer that is

... which could be a subject of a separate discussion

).... so you gotta start trying to record something. When you start and see/hear what you are getting - you'll learn allot on-the-fly and get better idea what this is all about as you go. Recording drums ain't like ABC or 2+2=4 ... , if somebody tells you, that all you have to do is: buy hi-end gear and 'read something and learn how' and then you'll be doing really good ... then this 'somebody' really does not know what he/she's blah blahing about or simply does not care really.
The problem also here is that to
tell you how to do it "right" or to describe how somebody personally does it - this would mean the same as writing long long article.... it's just too much stuff to describe and bunch of individual details and aspects.
treymonfauntre pretty much covered it for you ... in a sense. If you do not want or can not get yourself a multi-track recorder or a multi-input recording interface for your computer, then your option is to mic your drums, mix it all on your mixer and record stereo output from your mixer to your computer. If your mixer has mic inputs/preamps channels, then you don't really need to use your mic preamp-unit, but you can if you wish to try and see if it gets better than when using your mixer's mic preamps.
Set up your kit, place mics, connect mics to your mic-ins on your mixer, set some not-so-high/not-so-low level, set pan for your mics on your mixer (for example kick and snare - center, spread toms and hats/cymbals somewhat left/right) do not apply any eq on your mixer yet (- you can try messing with eq and most likely will want to do so later after listening to your test-try recordings), connect stero output to your soundcard input, fire-up your recording software, set-it to record, click record

grab sticks and hit the damn drums. Play something wild. Put down sticks. Click stop. Playback your recording. Take a good laughter or get pissed - what ever works better for you or what ever is least controllable by your personality. Have a beer or orange juice ...what ever is your regular drink. Relax.
Then you gonna try to adjust what ever is under you control trying to make your recording better - from mics placement, gain/pan/eq/or what ever processing through actually playing techniques and other things, like acoustics of your room factor etc...
While doing all this you may realize that it may be a good idea to record all your mics onto individual tracks and then mix it down so you have control and you can focus while you are listening and can adjust levels/pan/eq/processing in real time while listening - to bring it all nicely together.
And this is just to record the drums only.... no other instruments/vocals involved yet (if you plan on recording music/band/one-man-band). To record drums and then mix drums with the rest of the band - this is a real job... and then you REALLY would want to have control over individual mics (drums/symbals). If you record your drums already as 'stereo mix' ... then it will be very hard to do or even impossible.
okey ...blah blah ....
the bottom line, you have to START recording, see what you are getting and getting into, then post here again when you get any specific situation/question or what ever.
And what exactly your mixer is model/make? And what exactly your sound card is? And what software do you use to record? .... more detals you give - better chance to get specific helpfull answer to your question(s)
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btw, to avoid all this...there maybe a very simple and economical solution. Get rid of all your mics, mixer etc.... get just one mic, one pre and one recorder. Command all the band members to get on stage. Place the only mic you've got on the center-spot of the stage. Push record button on your recorder. Command the band: "Start Playing and Singing NOW!" And let Mother-Nature do the work for you
good luck and stuff