While there is no carved in stone way of doing rest-pause, here is an example of perhaps the most popular, and result producing way to do it (rep ranges vary).
Lets say you are doing barbell curls (easy example). You take a weight that you beleive you will fail at rep 8 with. If you only get 7, so be it, if you get 9 or 10 before hitting failure, thats ok too. For our example, after failing at rep 8, you simply put down the weight, and rest/breath JUST long enough to allow yourself to get about 2-3 more reps, do the same, and repeat until you hit 16 reps, and you are finished--cooked is a better word actually.
Different muscles require different rest periods for most people, but as long as the range is 15-45 seconds, AND IS DONE CONSISTENTLY from week to week, you are OK.