I'm not sure if there is a proper fitness regime because I know quite a lot of players that don't really do anything to stay in shape, but anyway manage to play somehow.
I on the other hand try to train nearly everyday by doing a combination of weight and cardio sequences. You need the weight part to be able to hold yourself on the horse and hit the ball etc.. The cardio part is really important too, because if you don't have a well trained heart, you will probably not be able to keep up for a whole game. And then of course I try to eat clean and healthy and barely drink any alcohol.