To tame a horse, first you need to find a horse. You can attempt to ride it. Press left shift to dismount.
The horse will keep throwing you off. Keep trying over and over again. After some tries, eventually the horse will not throw you off. If you can open your inventory the horse is now tamed.
Remember that you can not attempt to tame a horse while holding any items like hoe, shovel, pickaxe etc. It will keep you throwing off even if you try plenty of times. But once you have tamed a horse then you can hold any items while riding over it. Find a saddle and put it on the horse.
And now you can ride anywhere you like. You can also fit horse armour if you like.
