Rauke said it...
But I'm going to say it too, anyway.
Always START SLOW. (Don't think of that as yelling, just speaking forcefully.)
In fact, new shooters should be instructed to draw by the numbers.
Step 1: Sweep jacket or cover and grasp grip, keeping finger out of trigger guard.
Step 2: Release retainer (usually concurrent with 1.) keeping finger out of trigger guard.
Step 3: ... and so on.
Then after the student has done this enough times to want to choke the instructor, move on to one continuous motion, but slowly, emphasizing the correct movements - much like a martial arts kata. Which is EXACTLY what this is. (If handguns aren't a martial [from the root word for miltary, implying armed] arts form, nothing is.) Slow movements, emphasizing correct release of retaining mechanisms, movements of hand and weapon to avoid pointing it at self or partner, keeping fingers away from the wrong places, and coordination of both hands.
Speed picks up later. In fact, raw, blinding, astounding speed may not be all so important in most instances.