Maybe you should go and read the game guide

Hello and welcome Dinky! The best way to level your horses up is to make sure you train them once a week. I also usually enter mine in 3 shows a week. If after a few weeks they don't do well and don't seem to be improving, then I usually sell them and try to find better show horses. I hope this helps! I haven't been on this game as long as most of the other players, but I am starting to get the hang of it a little, so if you have questions please feel free to ask me. : )