HIIT involves high-intensity (and short) intervals—that's what it's all about. Warm-up is find ... so is cool-down. The stuff in between is what makes the difference.
The (mph) rates that you note—how intense are they for you?
The idea is to go all out for a
short period of time, then get some relief for an even shorter period (so that you can't totally recover). Since your rest time is not long enough to fully recover, each successive interval grows harder and harder. By the time you complete four intervals, you should pretty much be wasted.
Be aware that you should not simply jump into a HIIT program, if your body is not ready. Start off slow, but challenge yourself. Get your body used to activity at increasingly intense levels. There's no need to screw up your body by advancing your program at too fast a pace.
For a good look at a quality HIIT protocol:
In Search of the Ideal Aerobics Routine