The Expert riding is the first level of flying you can train. When you get to the level of 60, you can learn the skill, and it will allow you to fly at 150% speed. You should find a flying trainer first. There are many to choose from, but if you pick one associated with a faction you have a high reputation with, you will receive a generous discount. Your best pets can be Stormwind and Orgrimmar. And the riding skill will cost you 250 WOW gold . You will also need to buy a flying mount which is available from the vendor located right near the flying trainer NPC.
After you have learned the riding skill, and when you get to the level of 60, you can get your flight masters license. And then you can use the flight mount in Azeroth: Kalimdor and the Eastern Kingdoms. You can train the cold weather flying skill at the level of 68. This will allow you fly in Northrend, and you should have expert riding. If you become an artisan in riding, you can boost flying speed to 280%. This skill can be trained at the level of 70. And you should spend 5000 gold on it. If you are exalted with the faction of the flying trainer, you can only cost 4000g. You will also need an epic flying mount, which will cost you an additional 100g.
When you get to the level of 80, you can learn the master riding, and it allows you to ride an epic flying mount at 310% speed. Only a small increase over artisan tiding, the cost remains the same, and you can use the same mount.
Which flying skills do you need? Although the 150% flying speed from expert riding is perfectly fine for getting where you need to go, the faster flying does have its benefits. It may seem to be a luxury to the artisan and master riding, but you can save a lot of time. If you cost a few minutes a day to sell random loot on the auction house, you will have the fastest possible flying immediately. Also, you can buy gold from WOWGold4EUR, it can be the fastest way to get gold in the World of Warcraft.