First you just need a regular horse, you can spawn it with a egg or just find it. For the next steps I just want to say that you will need a saddle to actually control the horse when you ride it.
Then you want to go up to the horse and right click it. You will now be on top of the horse either you can press to get off and it will make you get off. You can't control the horse yet though.
Keep going on and off the horse, right click to get on and shift to get off, once you have done it for a little soon a heart will pop up on the horse. That you means you have tamed it.
Then as you are on the horse you want to press E, as like you are going to your inventory, after you press E it will have at the top left spots where you can put the saddle and armour.
Now you have your horse! :) Also with the armour you can pick to put on gold, iron, or diamond. I just chose diamond. But to get on right click and to get off press shift. Hope you enjoy!