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You'll want around 20 apples for each horse you need to tame. Apples make taming the horses significantly easier (and quicker) than attempting to tame them without food. Horses are typically found in flat, grassy areas such as Plains and Savannas. In your equip bar at the bottom of the screen, make sure you have the apples selected before approaching the horse. Right-click or left-trigger the horse until you stop hearing crunching sounds and the horse starts bucking and neighing. On Minecraft PE, you'll face the horse and tap Feed exactly 20 times. This will allow you to mount the horse. Right-click or left-trigger the horse to do so. You should mount the horse at this point. On Minecraft PE, you'll face the horse and tap Mount at the bottom of the screen. Once red hearts appear around the horse, you have successfully tamed it. At this point, you can dismount by pressing left Shift or the "Crouch" button. If the horse bucks you off, mount it again and wait for the red hearts to appear. You may need to do this several times. You'll need two tamed horses in order to breed them. If your first tamed horse isn't following you around, you can enclose it in a two-block-tall area to keep it from wandering off. You can use any resource (e.g., dirt or sand) to do this, but the wall must be two blocks tall in order to prevent the horses from running away.  If you have enough fencing material in your inventory, you can use that to enclose the horses instead of using blocks. You might want to leave some extra room in the enclosure since you'll be adding a third horse to the mix shortly.
Gather at least 40 apples. Find a horse. Equip the apples. Select the horse until it stops eating. Switch to an empty hand. Select the horse. Wait for red hearts to appear. Tame another horse. Build a two-block-tall wall around the horses.