It will stay in the area that you mounted it, unless directed to fly somewhere else via the world map. You will not be able to directly control how the Dragon flies. Once in the sky, the Dragon will begin a circular flight pattern, not unlike the Dragons you might see in the wild. Odahviing can be tamed and ridden by traveling to the Throat of the World where he circles the summit. Certain named Dragons cannot be tamed ( Alduin, Sahloknir, Paarthurnax, Durnehviir, and the Skeletal Dragon in Labyrinthian). Instead of crashing into the ground however, the Dragon will land very close to you, and by interacting with the Dragon (A on the X360), you will automatically climb on, and the Dragon will take to the skies. Once you have all three words, simply find a Dragon, either in the wild or at a Dragon Lair, and use the shout on the Dragon, much like you would using the Dragonrend Shout. To begin, you will need all three Words of Power of the Bend Will Shout, which are obtained by doing the Dragonborn Main Questline. The process involves using a Dragon Shout to cause a Dragon to temporarily become your ally, and speaking to it once it lands lets you ride it into the sky and almost anywhere else. Dragon Riding is a new feature in Skyrim: Dragonborn that allows the player to tame and ride Dragons.

Can you ride dragons in skyrim