Counting drum music is a relatively simple process that can be understood quite easily. The words "music theory" in essence can nearly paralyze the self-taught musician, especially percussionists grown accustomed to learning-by-ear. The benefits of learning how to count drum music can offer unparalleled effects once mastered. The concept of notes are applied to all surfaces (both drums and cymbals).

1. Begin by examining the whole-note which receives one whole beat per measure of music. in standard 4/4 timing (referred to as common-time or assumed when no time-signature is written) the whole-note is counted as one followed by four rests (do not play on a rest), when learning to count drum music.
2. The half-note is exactly half of the whole-note. In 4/4 timing, two half-notes would occupy all four beats in the measure. The beat is on one with a rest on 2, a beat on 3, and a rest on 4.
3. Quarter-notes, eight-notes, sixteenth-notes, thirty-second-notes, sixty-fourth-notes, and so on follow the same trend. When learning to count drum music In 4/4 time, 4 quarter-notes  occupy a single measure of music. The beats are played on 1, 2, 3, and 4. To play in time, acquire a metronome and hit on every click of the metronome to play constant quarter-notes. Two eighth-notes equal one quarter-note, four sixteenth-notes equal one quarter-note, eight thirty-second-notes equal one quarter-note, and so on. Eight-notes are counted 1 & 2 & 3 & 4 &; Sixteenth-notes are counted 1 e & a 2 e & a 3 e & a 4 e & a; Thirty-second-notes are counted 1 1 e e & & a a 2 2 e e & & a a 3 3 e e & & a a 4 4 e e & & a a; and the division is so on.
4. Notes can also be divided into triplets as well. A triplet is counted as 1 & a 2 & a 3 & a 4 & a, or 1 trip-let 2 trip-let 3 trip-let 4 trip-let. Further division of a triplet would be a sextuplet counted 1 trip-let & trip-let 2 trip-let & trip-let 3 trip-let & trip-let 4 trip-let & trip-let. Further division of the triplet is follows the same pattern. A quintuplet would be five beats counted 1 & 2 & 3 1 & 2 & 3. When learning to count drum music, an affective warm-up is to play through a division chart from whole-notes through thirty-second-notes to practice playing and counting OUT LOUD.
5. The concept of time signatures can be confusing when not understood properly.  4/4 or common time means four beats per measure. The top four informs that there are four beats in a measure, and the bottom four informs the division is in quarter-notes. Put simply, there are four quarter-notes in each measure. If the time signature was 6/8, this would mean there were six beat in a measure. The eight on bottom informs that the note value is eighth-notes, so there are six eighth-notes in each member. If the time signature was say 13/16 then there would be thirteen sixteenth-notes in each measure. If the time signature was 24/64, then there are 24 sixty-fourth-notes in each measure.
6. Expanding on the concept to odd-time-signatures. The concept of odd-time has a different feel since the average human is programmed to play in even numbers, this is why 4/4 has become common time. For example 13/16 would be odd time, has thirteen sixteenth-notes in a measure and may feel weird to play. What makes odd-time-signatures harder when learning to play is the need to pay closer attention to counting. Odd-time adds a completely different dimension to writing music, often creating a dissonant sound to the listener's ear.

With the basis of learning to count drum music understood, the challenge comes with different time-signatures and mixing and matching note values. Practicing the above concepts and mixing and matching time-signatures, and note values provide for more interesting and consistent playing. Apply the counts for notes to count rests as well to master counting music. Applying these concepts to the drum set is another lesson.

Resources:

Strong, J. (2001). Drums For Dummies. New York City: Hungry Minds