A quick and simple way to set up a drum kit with three microphones would be to simply add a snare microphone to any of the two microphone methods mentioned before. Here are other options:
Kick, Snare, and Overhead
When miking in this configuration, you are able to prioritize your sound to focus on two drums and capture the remaining ones with an overhead microphone. The first two microphones that we will place will be the snare drum and the kick drum, for both of which we will use a dynamic mic (set to cardioid). Point the first mic at the snare set about two inches away and direct it toward the middle. The second microphone will be placed inside the kick drum, positioned to your sound preference. You may decide to place it a few inches from the beater head, or you may want it closer to the outside of the drum head. For the overhead mic, place a condenser (set on a cardioid polar pattern) two feet above your cymbals and point down at your drum set.
X-Y Setup plus Kick
For this technique, position the microphones as you would for the two mics X-Y, again, two cardioid condensers making a 90-degree angle above the kit. The third mic will be a dynamic cardioid microphone for the kick drum. Place the mic inside the kick and adjust until you achieve the right amount of bass drum.