I taught my horse Domino some tricks. Nothing as fancy as the Spanish walk, but that would have been awesome! He knows how to smile, sing, say "yes", say "no", be bashful, bow, fetch, and shake.
I use treats when I am teaching them, giving them a treat for even the slightest try. Then I gradually give them less, ask for a few attempts or tricks before giving them a treat. That way they don't get pushy about it.
Teaching them how to say "no" is probably the easiest. You will have to choose a signal so your horse will learn to do the trick when he sees you doing the sign. For example, I would place my hands in front of me to signal "no", and my arms down for "yes". (This also works well when you are showing people your horse's tricks, because they rarely notice your movements). Using voice commands are useful also. What you will be doing is taking something and lightly poking or tickling the horse's withers with it. What to use really differs with each horse, some horses you can use your fingernail, and they will shake their head. Others you might have to get something pointer, just make sure it is blunt and can't hurt the horse. When the horse shakes his head, immediately give him a treat. and repeat.
For "yes", take a treat and get the horse's attention. Now that he is interested, move the treat up and down slowly, trying to get him to "follow" the treat. Make sure you are showing him his cue while you are teaching him. After a few tries, just show him the cue and see what he does. If he moves his head up and down even slightly, give him a treat. Before you know it, your horse will be nodding "yes" like crazy.
"smile" is pretty easy. You can either get something that smells "funny" to a horse and put it on their lip, and when they "smile" rewards them. The only thing about that is they only do it a few times. But you can also just take a treat and hold it above the lip. Some horses will raise their lip and try to get it just like that. Others will probably raise their head and try to reach it, but their neck can only stretch so far. After that, they will try to grab it with their lip. Remember, reward the slightest try.
I'm getting tired of typing... lol..
Hope this helps.