You cannot fast travel on a dragon to a different worldspace. The dragon will then either aid you in combat, attack you, or simply leave. Once given the command to land, the dragon will return to ground level where you can dismount. In terms of in-game time, fast traveling on a dragon is almost immediate. To fast travel to different areas, simply select the location on your map as you normally would. The use of weapons (such as bows and melee weapons) are mostly limited as well. Area of effect spells or summons cannot be used while riding a dragon. The dragon will then use a standard aerial attack pattern and can be assisted by you via shouts and spells. You can lock on to a single enemy which causes the dragon to attack that target. After you do this, a help section will be added in the menu for dragon riding. Unlocking the third word of the Bend Will shout starts the final quest of the Dragonborn main questline, in which you're likely to ride your first dragon. You cannot directly control the dragon while riding, but can give it certain instructions. The dragon will then land and allow you to climb onto its back and ride it.
In order to ride a dragon, you must acquire all three words of the Bend Will shout and use it on a dragon. Dragon riding is a new gameplay mechanic added by the Dragonborn add-on.
