Record the drums in an organized fashion using a mixer and several microphones. Place the microphones near the drums and cymbals and record each drum and cymbal, including bass drum and high-hat on a separate track. Partition the drum kit into sections if you do not have enough microphones for each item.
Add two overhead microphones to get a stereo sound for the whole kit. Check the levels of each microphone and record. Watch the levels so that you get a good, undistorted signal when recording. Name each track according to what is on it.
Edit each track individually first. Get the best level you can and modify the sound using effects. You may want to wait until later to add effects on the entire kit. Use any available mastering functions in your software to enhance and improve the recorded sounds on each track.
Mix the bass drum with the high-hat and snare to get these tracks working together at the correct levels. Add the toms and cymbals into the mix. Mix in the recordings from the two overhead microphones. Adjust the levels so that everything sounds as it should. Watch for peaks and boost levels that are too low. Use a gate effect to reduce sound bleeding in from other sources on any track.
Render all the tracks used to record the drums into one track. Play the track to check your mix. Use signal enhancing functions in your software to normalize and compress the signal if you want to boost loudness, for example.
Add the drums to the other instruments using these settings if you are satisfied with the mix. Adjust the levels until the drums fit with the levels of the other instruments.