1) Go to the Chocobo Stable in Jueno. Make sure you have 4 gheslbit grasses and are level 20.
2) Talk to Brutus in the stable.
3) Brutus will ask you some questions, choose the first answer and then the second answer.
4) Next talk to Osker who is nearby. Osker will tell you that you need the greens (grass). Since you have the grass you are already prepared.
5) Next go up to the Chocobo near Osker and trade one of the green to it. The Chocobo will squeal and most likely not eat the grass.
6) Note the current time, you must wait until the next day to try again. When time is past 0:00 (not exactly) trade the grass to the Chocobo again. It will reject this time as well.
7) Repeat the process each day, attempting to feed the Chocobo each time. Once he begins eating feed him one grass each day. Once you have fed it all four of the greens you will get your license!

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)