How do I ride my mount in World of Warcraft?

You can get a horse (depending on your race) at level 20, you will get an in-game mail telling you where to go for your mount. Humans have access to the normal horses while the undead have access to the undead horses (Horses that are just skin and bones).

Death Knights, Paladins, and Warlocks have their own versions of horses available from trainers and quests.

You can also get a horse type mount from certain holiday bosses and events (Headless Horseman from All-Hallows Eve event, and The Baron from the Stratholme instance).