Before attempting to record using an overhead microphone, ensure that the drum is tuned and sounds good. Using a drum key, tap around directly inside the drum head next to the tension rods. Move around the drum in a circle and adjust the tension so that the drum has the same pitch all the way around. Turn the drum key in a clockwise motion to raise the pitch and use a counterclockwise motion to lower the pitch. It will do no good to mic a drum that isn't properly tuned.
Use a microphone that matches the frequency response of the instrument. Snare drums have a frequency response between 100 hertz to 12 kilohertz. Bass drums are between 50 hertz and 5.5 kilohertz. Cymbals are between 300 hertz to 17 kilohertz. Toms have a wide frequency response ranging anywhere from 500 hertz to 10 kilohertz. Look at the specifications on the microphone itself; there should be a list of the frequency response range on the side. By matching the frequency as close as possible, you can ensure that the high and low frequencies of the instrument aren't cut off.
For cymbals, you want to place the microphone about one foot above the center of the drum set. Place the cymbals to the right or left of the set to catch the ambient frequencies. Each drum should have its own microphone about a foot above the actual instrument. The exception is the bass drum, in which the mic must be placed about a foot above and in front of the drum head.
To prevent other instruments from getting picked up by the microphone, cut a piece of cardboard about 11 inches by 17 inches long. Fold the cardboard into a trifold with four inches on the sides and place it directly behind the microphone. This will help to reduce any external frequencies and help isolate the sound of the individual drum. This technique makes it easier to change levels on a specific drum component as well. For instance, if you want an additional bass sound, you can turn up the track that's attached to the bass drum microphone.