We are actually not owning our own studio. We have just put up a homebased
recording equipments together, so we'll end up with a home-studio.
The thing is really easy.  Just use some SM57-Shure instrument-microphones
on the drums / speakers (also works good with vocals too),
connect them to your mixer, and connect the mixer to a computer/another
recordingdevice, and you're in. The sound quality will not be like
original recordings from the real studios  but ... hey, demo-recordings
aren't supposed to be the best quality either.

Watch your cabling, so it wont be looking like this:

Actually, since cables are expensive in the lenght, take care of them.
Try to put them away, or hide them so you don't step on them , or bends them.

SM 57 Shure Microphones

Zoom8080 Guitar Multiple Effect Processor

Guitar Amplifier usually give better sound than playing directly into the mixing device or computer. Use a SM57 to record this sound instead.

For best sound performance, please use a DI-box between the bass and the amplifier, so you have an alternative line into the mixer.