How do you start to train your horse to do things like that? A good relationship is the first thing, but what next?
Well the following step is probably starting by some small, quick and easy tricks, because you need to get your horse to understand what you want and reward him when he does something you want so that he's able to associate the reward with the exercise. You can use any rewards you want, some people prefer not to use treats, which is totally ok, you can reward by just cuddling, but of course horses prefer treats and you'll get more attention from him by using some of them.
Some small and easy tricks are smilling, jambette, hugging, kissing, picking up things, saying yes or no (although I do not really like this one) etc.
And it's important you break the exercise in small parts, for example, if you want him to pick up a whip the first step would be dropping his neck > reward, then dropping his neck and smell the whip > reward, then dropping his neck and playing with it with his mouth > reward and then dropping the neck, playing and grabbing it > rewards!
So this basically it, start small and end big :) Leave the more complicated exercises when the horse is already focused on his ''job'' :)
It takes time, dedication and patience. Took me one year and half for my horse to learn spanish walk, that was our first trick and I had no idea what I was doing ahah! Once my horse started to get the idea what I wanted things went very fast :)
Best of luck!! :)
Zexious, I have a youtube account if you want to check more videos there :)