First of all, we go through the components of the kit, their names and the sounds you can get out of them. Once that's done, I'll walk them through proper posture, grip and stroke; then the 8th note rock beat, counting, right hand transitions around the kit, opening and closing the hi-hat, bass drum variations and basic fills; basic sticking exercises; 6/8 grooves and fills; 16th note grooves with a) an 8th note ostinato b) a 16th note ostinato with one hand and c) a 16th note ostinato played hand to hand; shuffle grooves and half-time shuffles. We always use a lot of reading material.
After dealing with a lot of three-way coordination material and fundamental pop/rock styles, we'll start going through them again, but this time I'll have my students pedal quarter notes (or dotted quarters in 6/8) throughout the grooves and fills. Later on I'll have them play the same grooves and fills with an 8th note upbeat ostinato on the hi-hat pedal. Then we'll start working on adding open hi-hat sounds into various grooves, going systematically through all placement possibilities. Once the student has acquired some skill and knowledge through the more common playing styles, we can go into more "exotic" styles, such as jazz, salsa, samba, Oakland funk etc...
I don't like to incorporate rudiments and technical exercises in my teaching. In my opinion, there are a lot of more important things to learn before starting to fine tune one's technique. Of course, I'm constantly pointing out technical issues and giving practical advice on how to achieve certain things with greater ease and relaxation, but I don't enforce a strict practice regime unless the student explicitly wants to improve his technique. Music should always come first.