I found this info from here on how to tame horses. You can tame a donkey using the same method to tame a horse:
To tame a horse, approach it with nothing in your hand and right click on it. You will now be riding the horse&emdashfor a second or two, until it throws you off. Try again, and again, until finally you see some red hearts and the horse lets you stay on.
It usually takes 3–5 attempts, but you may be luckier or unluckier than that. You can make the process quicker by feeding the horse first.
In addition:
Only tamed horses can be bred. To make horses breed, feed them golden apples. They will go into “love mode” and make a baby.
I also found this information from the Minecraft WikiMinecraft Wiki, which states that two donkeys can be bred together in the same fashion as breeding horses:
Breeding two donkeys creates a donkey foal. Since all donkeys have the same texture, the offspring will look exactly like its parents when it is fully grown.