Train Mount 1 (Source)
Section 10 - Mounts
Certain types of pets can be trained as "mounts," which will allow the pet's owner to ride around on it. Needless to say, this is incredibly cool and highly recommended. Normal mount walking speed is faster than a player's running speed, and the mount equivalent of burst run (called "gallop") is faster than a player's burst run (and tends to last longer).
You can't make just any pet into a mount, however. At this time, the only creatures that can be mounted are: Dewbacks (Tatooine), Bols (Dantooine), Kaadu (Naboo), Carrion Spats (Corellia), Falumpasets (Naboo), Humbabas (Corellia/Talus), and Brackasets (Dathomir).
All variants of a mountable species will work (i.e. dewbacks, lesser dewbacks, mountain dewbacks). Entirely different species that are similar in appearance will NOT work (i.e. NOT bagerasets, bolmas, mawgax, etc).
Anyone can own and use a mount (if they have enough skill to control it as a pet), but only a Creature Handler with the Group Management IV skill can teach it the "Mount" command. Non-CHs are limited to creature pets CL 10 and below, but fortunately each currently mountable species has such a variant in the wild (lesser dewbacks, lesser plains bols, motley kaadu, carrion spats, plodding falumpasets, and lowland brackasets).
A pet has to reach a certain size (which varies by creature) before the Train As Mount command becomes available in its training menu. In most cases this will be around 50-75% of its total adult growth, though some of the larger variants (like giant carrion spats and savage humbabas) may be mountable much soon. Giant carrion spats in particular can be made into mounts immediately after taming, making them a popular choice among Creature Handler salesmen. When a giant carrion spat reaches a certain size, it can even become too large to be used as a mount. When this happens, the owner will receive a one time pop-up box asking if he wishes to stop its growth, or no longer have it function as a mount. This is your only chance to decide, so make sure you choose carefully.
You can climb aboard a mount by choosing "Climb On Mount" from its radial menu, or targeting it and typing /mount. You can dismount by choose "Dismount" from the creature's radial menu, or typing /dismount. You can still engage in combat while mounted, but you will be unable to use any of your special profession moves. In addition to being limited to default attacks, your mount will drastically slow down to prevent you from attacking while keeping out of your target's range (a.k.a. "kiting").
While mounted, you can give your mount a momentary boost of speed by typing /gallop. You cannot attack while galloping, but you can still be attacked. Since you cannot attack, however, the normal speed restriction while in combat is not in effect (making this a handy way to escape from tight situations). After a few moments your mount will become "winded" and return to its normal running speed while it rests (just as with a player's burst run ability). You can end the gallop earlier by using the /gallopstop command (for example, if you are already galloping and wish to stop to engage in combat).