One of the biggest problems facing the budget recording artist is getting the cymbals to sound, well, like cymbals. You may need to tighten the cymbals down on the stands to limit the movement, and I suggest you buy fresh felt washers. Setting up a normal microphone is difficult, since you can get wave-effects due to the cymbals natural movement after being struck. If you set up the mike below or above the disk edge, you may need to normalize the channel to prevent noticeable volume changes as the disk changes relative distance to the mike diaphram. If you need to use a standard mike, I always set it up so that it was slightly offset from the center, over the top of the cymbal.

If you have the time, do a search for a special type of microphone called a Pressure-Zone Microphone (PZM). Radio Shack actually carried these for a couple of years. They work great (particularly for cymbals), and they can be used to augment the overall sound of the set if you have two extra channels. Keep an eye on places like eBay, you can get them cheap.

As for the rest of the microphones, if you want to record a great sound, you must get a great mike. Bass drums in particular are exceptionally difficult to get right, most of the time it sounds like someone beating on a muffled coffin. You can rent microphones relatively cheap, and if the song you're recording will be used as a demo, spend the little bit extra to make it sound as good as possible.

I used to double-mike my snare drum, one cardioid pointing towards the center of the top and one omni near the snares underneath. You can balance the snare attack and get some interesting effects, especially if you put a reverb or delay on the snare side. The top mike can pick up some of the stickwork and backbeat, which is a great way to get those "little things" into the mix.

Another oft-overlooked thing is to buy a can of oil. Nothing shows up in your demo better than a squeaky bass drum pedal or hi-hat stand.