There is a chocobo stable in each major town (three in Jeuno) and at most crags. Talk to an NPC standing near a chocobo, and he will give you the current rate for rental (it varies depending on how many people have rented a chocobo within a period of time). If you select Yes, you will see a short cutscene of yourself getting on the chocobo and leaving the stables. You will then be able to ride the chocobo for the amount of time that is your level, with a 30 minute max (ex. if you are level 24, you will be able to ride the chocobo for 24 minutes. If you are level 45, you will be able to ride the chocobo for 30 minutes)
Your Chocobo can dig for it’s food as well as items. Digging requires 1 Gyashl Green so use them wisely. When you attempt to dig be sure you are in a soft area such as sand or dirt, hard packed ground is no good. If you are in the right places your Chocobo may even find an item! The items your chocobo finds is based upon the area, if you are near water you are likely to find a water item; if you are near the desert you may find an earth item.