Jazz drumming is often regarded as difficult due to its triplet based time feel. Generally the right hand plays the ride pattern while the left hand comps. Playing a constant ride pattern without having to think about it is the key to being able to separate your hands and really improvise on the snare freely. Many, many jazz drummers use comping patterns made from 3 simple basic ones. I crudely illustrated them here, and provided midi files of what they should sound like if you click the diagrams. Practice these extremely slow at first, focusing on consistent sound and accuracy. Eventually you'll build them up to speed. The *'s represent rests in the triplet (remember all 4 beats in a bar of swing time are subdivided into 3 triplets). Note: The first two bars are the same as the last two bars in all of these, but I wanted it to be a full 4-bar figure:
When you comp, simply chop these left hand patterns apart and rearrange them while keeping the ride pattern constant.
Here's a midi I made of some example comping using strictly these 3 patterns.
Now if you don't know what to play with the bassdrum, an easy way to start is to simply play it instead of the snare drum every other note, also while keeping the ride pattern constant. Occasionally play two in a row to alternate the up or downbeat emphasis.
Here's a midi of the same comping example from above using this bassdrum technique.
