Special consideration is needed when recording drum kits. Drums, like all acoustic instruments, need to breath. With the exception of some dance music and electro-pop, you cannot get a satisfactory result from a dead space. The best solution is a properly designed live room. Ideally you need at least eight feet of space above a kit. The room should be live but not roomy or boxy. Roomy, boxy sounding recordings are caused by standing waves resulting from the placement of acoustic instruments in an ordinary shaped room: ie a square or oblong box. Proper studio live rooms are constructed avoiding parallel surfaces and thus avoiding the production of standing waves. The ideal room size for recording a drum kit is about 2730 cubic feet with mixed material walls and a sloping hard (ceramic) ceiling.
Unless a drum kit is properly tuned, no amount of messing around with mic positions and EQ-ing will get the desired result. The drum should sound good straight away. If it doesn't, it needs attention. Not all drummers know how to tune a kit. The recording engineer should know how to do this.
Top Kit - Cymbals
For Rock, Metal and Pop, you need between 8 and 12 mics to record a drum kit properly. Jazz, R and B, Folk or Blues each require different approaches. Overhead mics should be a high quality condenser such us AKG C414s or AKG 451s placed directly over the whole kit about 2 or 3 feet above the height of the tallest cymbal. The Hi-Hat also requires either a directional condenser such as an AKG 451 with a hypercardioid capsule, or special dynamic such as those recommended in the Audix range by the manufacturer.
The snare would normally use a dynamic microphone placed just over the rim of the drum and pointing to the centre of the skin. The Audix range of dynamic mics are a good bet but a Shure SM57 or 58 works very well. A lot of engineers and producers like to mike the bottom of the snare as well, usually with a high SPL condenser. Again, tuning is the key to a good snare.
Much of the toms sound will come from the overhead mics, which is why their placement is crucial. The rest of the toms sound comes from being individually miked, using a similar technique to that employed for the snare. One would normally use the same range of dynamic mics for this job. Again, tuning is an essential ingredient.
The Kick Drum needs purpose designed microphones with very good bass response at very high sound levels. AKG D12, D120, Sure Beta 52 or Sennheiser MD421. It is fairly normal practice to use two mics on a single kick drum. One to pick up the wallop and one to deal with the click. For many types of kick sound, the front skin will need to be removed and the skin tension adjusted to suit. The type of beater fitted into the pedal makes a lot of difference as does the amount of damping applied inside the drum. Your engineer should know all about this and what he needs to do to get the sound you are after.