Get wheat, carrots, or golden carrots
Approach a horse slowly
Right-click the horse to try mounting it
Dismount and mount again if it throws you off
Feed the horse wheat, carrots, or golden carrots to speed up taming
Keep feeding until hearts appear and the horse becomes tamed
Put on a saddle if you want to ride it without needing to keep taming
Right-click the tamed horse with a saddle to equip it
Ride the horse by right-clicking it while mounted with the saddle