Traveling
The only area you ride chocobo in Final Fantasy XIII is the Gran Pulse region. Your riding chocobo will not travel outside of this particular area so you will have to dismount if you need to travel elsewhere. You have to navigate around enemies while riding the chocobo or risk getting thrown off of the bird. Each chocobo has a small morale meter that decreases each time you run in to an enemy. If you deplete this meter, your character is thrown from the chocobo and you'll need to find another one to ride.
Treasure Hunting
When you mount a chocobo, you open up the treasure-hunting feature. When you get near a treasure chest a yellow exclamation mark pops up by the chocobo's head. Stop your ride and examine the direction that the chocobo's head currently faces. The chocobo will point directly at the treasure chest. Once you receive the treasure spot, your chocobo digs down to the chest.
Access
While you will see both Cocoon and Gran Pulse chocobo throughout your game, you do not receive the item needed to ride the chocobo until after the 14th mission of "Final Fantasy XIII." Once you complete this mission, you receive the Gysahl Harness, which opens up the riding dialog when you approach the chocobo.
Locations
The Archylte Steppe in the Gran Pulse region contains all of the riding chocobo. Most of the chocobo are specifically concentrated in the Font of Namva part of the Steppe, which is the area for an earlier mission before you gain access to the riding chocobo. Some areas in the Steppe are completely inaccessible without the chocobos, as they can jump great distances among the cliffs in this area.