Piaffe can happen in a variety of ways, so I will explain what I did with Tam. It is certainly not the only way!
Tam began to offer Piaffe from Goat on a Mountain...now, it was not correct or pretty (he was all bunched up underneath himself and could hardly lift his hind feet), but it was an offer that was gladly accepted! So we began to play with ways to elicit it that would perhaps cause him naturally to offer it in a more balanced way (so he could also lift his hind feet) and I because it is developing, then I try to keep it moving forward slightly and click and reward only a few steps. I do not ask for many steps because it's tiring, and they get worse the more I ask for. All of the following is done on the ground.
1) Original way it happened was a Goat on a Mountain that I added "energy" to. That is, he was in a Goat with a nice upward stretch, in ramener, I bounced beside him and brought my whip up and down rythmically. He started only by moving a couple of marching steps with his front legs. I would reward all attempts, even if only ONE foot is involved. I can also tap lightly under his belly (which also helps to lift his back for some reason). Too much energy concerns him...so the energy from me has to be controlled and not explosive or harsh of course. Neither can it be too soft...I'm not sure how else to describe it other than to say it is strong but it is held within me and not really directed AT him...so he is invited, in a sense, to join me with HIS energy. In tapping under his belly, if tap too much, he no longer sees it as fun, but rather annoying, and would prefer to do something else.
2) Transitions...Another way I elicit is is to trot with him, then I see how slow we can trot...but I do not slow to a walk myself, rather, I use alternate rising one heel (mine, I mean) then the other and dance/march softly...I don't bounce a lot...so the action from me is more from my hips and knees and ankles, and again, I will raise and lower my whip in rhythm to my steps...I will also smooch to him with each step, the same sound I use to ask for trot. But because I am not moving forward much, neither does he and again, he will bunch himself up and give a few steps. I keep it moving forward or he will bring his hind legs so far under himself that he literally gets stuck there and cannot use his hind legs much (all his weight is on his haunches). In this method (how slow can you trot "with energy", I again only ask for a few steps and then I ask him to trot forward again (normal, forward trot) then I click and reward. This idea I got from Walter Zettl dvd's...he trains the horses slowly, a few steps, and then into a forward trot before they lose the impulsion. There is much magic to be found in transitions...between gaits and within gaits (faster to slower). The key is in only asking a few steps of each gait or speed of gait before a transition. So the transitions are quite rapid. So not can piaffe happen, but in that realm of transitions is where the passage and suspension lies!
3) Lateral work...if Tam is well balanced and we are working on shoulder in, he will sometimes offer it then (I think because he gets bored with shoulder in). I immediately reward although it messes up our shoulder in. But again, I wish to develop his desire to offer and so I reward whether I've asked for it or not, because it simply all helps toward his development and understanding of the piaffe. Some would say that I perhaps shouldn't reward Tam for offering Piaffe when I am asking for something else, but in this "horse driven" method (horse has a say in the exercises), I don't mind breaking conventional rules. Tam may in fact be avoiding shoulder in by offering Piaffe, and I may in fact be rewarding him for trying to escape an exercise...well, really...my response would be "so what?"
Tam MUST always have a say in what we do and for how long we should do it, so if he offers a "developing piaffe" when I am asking for Shoulder in, then he IS, in fact, stating his opinion, and I should listen to it. It may mean that I have asked for Shoulder in for too many steps, because he never, ever refuses to try and if he offers Piaffe, it is after I work on shoulder in for a little while. So it could just be his way of saying "enough, let's do something else".
I will have to check back in my diary to see if I remember the beginnings of Piaffe with Tam correctly!
It has gone differently with Cisco. He still cannot piaffe in place (and he flat out refuses to do it in hand), but under saddle he can passage better and better all the time. So with him, I simple play with stalling the passage...again, only a few steps then forward again and reward, reward, reward.
So these are just some ideas. But if you would like to play within transitions to see what develops, then just remember to keep the transitions short. Hmmmm...I have not explained that very well...say you want to do walk/trot transitions. Walk for many steps, trot for only three or four or six, then right back to walk. Walk many steps, then trot again for just a few.
In trot/trot transitions where you are changing speed or length of stride, then perhaps go for faster trot for several steps, then slow down for just a few, then faster for many steps. Does that make sense? Again, I do not know if that is absolutely correct, but that is what I do.
When incorporating canter into the transitions, if you make the canter the "few steps" (or in this case perhaps only ONE step) and walk the "many steps" you will begin to develop some really beautiful and soft canter departs which are more and more balanced and collected. So again...laterals build strength and transitions build magic!