Why the 'right' after exercise? My impression is that not doing it at all is both more common and more harmful than doing it in a mediocre way.

I've seen many people do a slightly wrong thing once and throw their bodies out of whack for days or weeks, if not longer, when weights are involved. With cardio, you can pretty much do what you want with cycling without too much risk of injury (aside from falling or collisions) so long as you don't overdo it. But with cardio in general (running, swimming, cycling), people often get too excited and start off wrong, or have wrong form in running, and either injure themselves or exhaust themselves and drop out.

No matter what the exercise is, ease in, find a trainer (you don't need one for long depending on what you're doing), and be smart.

Bad form can cause injuries which may leave you worse off than before.