Crafting & Profession Mounts
Profession mounts may be obtained or created by characters who are very skilled in certain professions. Some of these mounts are crafted by the player, others (such as the Fishing and Archaeology mounts) are obtained by employing the skills of that profession.
Some mount items are bound to the original player - so you must develop the related profession in order to learn them - while others can be sold and traded. Some mounts require you to be skilled in the related profession in order to use them (especially Tailoring and Leatherworking, plus a couple of Engineering mounts), while others can be used by any character on your account. We usually indicate above the mount whether it can be traded or is bound, and whether it requires a specific profession to be able to use.
Recipe: Vial of the Sands can be found (rarely) in Canopic Jars gathered via Tol'vir Archaeology and is bound to the finder. This means an Alchemist must also advance Archaeology in order to learn to craft this mount, but the Vial of the Sands itself is tradeable and can be learned by any player.
Several mounts may be found (rarely) through Archaeology. All are bound to their finder.
Clearly the Blacksmith creates the harness, not the beast!
Engineering was the first profession to craft mounts and still offers the greatest selection. All are tradeable, and only two require any Engineering skill to use.
Engineering & Blacksmithing
Fishing up aquatic mounts requires a lot of patience! All are bound to the angler, so you must earn them yourself. Most do not require any particular fishing skill to obtain, however, so you can fish for them and level fishing at the same time.
Skilled Jewelcrafters can produce this beautiful set of stone panther mounts, that may be traded and learned by any player. The recipes may be purchased after achieving reputation with Order of the Cloud Serpent.
It may seem strange to create a mount through Leatherworking, but the Leatherworker creates the saddle, not the beast! In both cases the mount is bound to its creator. The Dustmane requires Leatherworking to ride, while the Elderhorn does not.
Tailors have been crafting flying carpets since Northrend. Sadly all require tailoring to use.