There is a riding trainer for each race. He can be found near the starting zone and usually just outside the nearest capital city. The Night Elf riding trainer is an exception. He is within the city of Darnassus, near the druid class trainers. The Orc riding trainer is also an exception. He is inside Orgrimmar near the hunter class trainers.
Mount prices have been reduced considerably so you can buy more than one if you would like a variety of colors.
Horde members will find this trainer in Thrallmar, while Alliance players will find him in Honor Hold. Buy a flying mount to go with your skill. Again, the vendor is standing next to the riding trainer.
This skill increase allows you to purchase the flying epic mounts, giving you a 280 percent speed increase.