As with most things, there is no 'one way' to play drums and no 'one size fits all' way of teaching drums. Below are a few of my thoughts and observations from watching people learn.
Making a noise (or preferably, a beat!)
The first thing I usually do is ask people to have a hit and show me anything that they can play. Some people are happy to play a few beats that they remember learning in school, others say they don't know anything and are too shy to hit the drums at all.
If people do play something, it is a good opportunity to observe their natural hitting style, technique, sound, rhythmic knowledge, and coordination.
If the student doesn't have any ideas, and we are luckily enough to have more than one drum kit in the teaching space, I like to just start playing a few simple ideas and getting them to copy. Then low and behold within a few minutes, they are up and playing a beat. Playing drums is not hard.
The first thing that I am looking for students to be able to do is to play rebounds strokes around all the different surfaces of the kit.
For me, technique it a means to an end, so I don't usually start worrying about technique until it becomes an issue. However for most students that is fairly immediately, so playing together and asking students to copy my strokes while talking about what I am doing is usually a good way to get students getting a feel for what it is like to allow the stick the freedom to rebound out of the drum.
The key concept at this point is fulcrum. That is having a pivot point on the stick between the thumb and forefinger and allowing the stick to behave like a lever and rebound out of the drum. With a little movement of the wrist to get the stick moving, we allow gravity to pull the stick into the drum and then allow the bouncy drum head push the stick back into its starting position. To achieve this we need a light grip on the stick, fingers open and not clenched on the stick and a nice loose wrist.
I usually get students to start with full strokes (the stick traveling through 90 degrees.) This helps to produce maximum energy into the drums and therefore maximum rebound out of the drum. That should help to make it easy to feel the stick wanting to rebound out of the drum
I will often tell students that I don't care how they hold the stick - All I care about is the sound they create.
Technique is not the goal - creating a good sound is the goal.
Creating a good sound includes being able to play to play quickly, slowly, evenly, loudly and softly. Pretty quickly when students try to do these things it is not long before the begin to realise that if we want to be able to control the stick to that degree, the way in which he hold the stick and make the stick move soon becomes an important factor
There are basically only two sticking patterns, single strokes, (RRRRR or LLLLL or RLRLR or alternate sticking) and double stokes, (RRLLRRLL) and combinations of the two which create our paradiddle patterns. And these are the first sticking patterns that I get students working on. Firstly on the practice pad if possible (because it is quieter) and then using all the different surfaces of the kit.
As students begin working on these patterns usually discussion of technique come to the fore.