Miking The Kick:
The best way to find the perfect spot is to listen in the control room while your assistant moves the microphone around. As the drummer plays the kick drum, you listen for the sweet spot - you will know it when you hear it. When you hear it, tell the assistant to stop. that is the best starting point.
For a heavier rock sound, you might put the microphone a few inches from the inner head, then baffle off the kick drum. For a more jazzy sound, you might leave the front bass drum head on, then place the microphone a short distance from the front head in a more open environment. Don't underestimate the importance of a good kick drum sound. It carries the downbeat of the music. This is what people dance to.
Miking The Snare Drum:
A loud snare drum's high transients mean that a dynamic microphone may work best. Start by aiming the microphone across the drum head toward the center of the drum where the stick meets the head. Keep the microphone about an inch above the rim. Maybe aim the microphone off center to eliminate some of the click and to coax more of the tonality from the drum. Listen and move the microphone to suit your needs. Aim the snare microphone off-axis to the high-hat to minimize leakage.
Miking The Tom-Toms:
Dynamic microphones work well on close-miked tom-toms where the player hits hard. Condenser microphones sound good on less aggressive styles, as they capture the player's rich subtleties and dynamics. Close-miked condensers may overload.
If possible, use the largest capsule microphones on the lowest tom-toms. Pull the microphones back some to capture resonance from the tom-toms that may be lost with close-miking. The farther away they are, the more the rest of the drums affect the sound, picking up more of the bulk of the drum. The tom-toms won't lose as much low resonance through the floor.
Lower the ringing in the toms by tossing a handful of cotton balls inside the toms. Ringing decreases depending on how many balls are tossed in. Even properly tuned toms can ring out. Try hanging the drummer's stick bag off of the side of the floor tom to reduce rattle.
Tips I've learned from drummer friends and sound teams along the way, to share with you that great sounds can be gotten with a few microphones!
Great resources I have recommended to my drummer:
Play Drums by Ear
All the best,