Don't want to interfere with discussions on how to instruct, but here's how I was instructed, and what I read to myself, aloud before every flight, well, perhaps not aloud if there are sensitive souls aboard:
1. Engine failure during start run: Power off, get off the rwy if able
2. Engine failure after takeoff and under 500 ft AGL: Nose down IMMEDIATELY, full flaps, land wherever possible
3. Engine failure above 500 ft AGL: Standard procedure - which I then go through.