They are extremely hard on the horse's body and take it takes years of conditioning and training to get a horse to the point where they can actually be able to hold their body in order to execute them properly without doing any damage.. so DO NOT TRY THIS AT HOME.. at least, not without professional help. I sure didn't!!
I was able to do a piaffe on the stallion I used to ride, and at the most basic level, I just thought of creating a "wall" with my aids, while asking him to keep trotting. That is as basic an explanation as you can possibly get, but the aids are really much much tougher. You have to "grow taller" in your saddle, ask the horse back on its hind end, and use diagonal aids to keep asking the horse forward... very complex.
The passage is kind of just an extension of this.. the horse keeps moving forwards with a higher, "springier" stride.
Again, this is about as basic as I can possibly get. I'd write a novel otherwise Hope this helps a tad?