Find two adult horses or two adult donkeys
Tame each one by riding it until hearts appear
Hold a Golden Apple or Golden Carrot
Feed the same breeding item to both animals
Wait for hearts to appear
A baby horse or baby donkey will spawn
To breed a horse and a donkey, tame one horse and one donkey
Feed both the horse and donkey a Golden Apple or Golden Carrot
Wait for hearts to appear
A mule will spawn