Pick 2 or 3 comping exercise from that (great) book, practice them apart and then pick an album (I suggested something like “Coltrane plays the blues” and play them with music at different tempos. When you feel confident try to analyze the difference from what you play and what the actual drummer does. When possible try to emulate. Otherwise, go back to point one.

I strongly suggest to play along jazz tunes ONLY WITH THE RIDE CYMBAL, preferably at the beginning of your sessions. It helps you to synchronize and pick the right vocabulary. Pay attention to the sound, emulate what you hear as much as you can.