Instructions
Decide what type of flying mount you want. There's a lot of variety in "World of Warcraft" flying mounts, from rockets, flying carpets and multicolored hippogryphs to majestic dragons, proto-drakes and phoenixes. The only mount type you don't have access to is the Alliance-exclusive gryphons.
Identify what you need to do to obtain the mount you want. Some mounts, such as flying carpets and flying machines, require you to have a specific profession, while others, such as nether rays and some types of drakes, require you to increase your reputation with a specific faction. Other mounts, such as most proto-drakes, are rewarded when you complete an achievement, while others can only be found as a rare drop in a dungeon.
Perform the required steps to obtain the mount. Some mounts may be obtainable in a day or two, while others require months of daily effort or, in the case of mounts obtained in dungeons, a healthy dose of luck. The exact steps to get a flying mount vary wildly depending on which flying mount it is. For example, you might have to kill a boss in the mount you want until the mount drops, or increase your reputation with a certain faction to exalted through daily quests or killing enemies.
Repeat the process with any other mount you want.