To catch a chocobo, first you need to make sure that one of your active characters is equipped with a Chocobo Lure materia. You can buy this materia from the Chocobo Ranch for 2000 gil the first time you go there. (note: you can only get up to two copies of this materia, so do not sell it...unless you want to)
After, find an area on the world map where there is chocobo tracks on the ground. (different areas have different quality chocobos) Chocobo quality ranges from "Poor" to "Wonderful".
After you have found this area, walk around on the chocobo tracks until you enter a battle with a chocobo in it. Eliminate the monsters while distracting the chocobo with some greens bought from the Chocobo Ranch. (near Kalm) After the battle, dismount your chocobo and choose the option of sending it to the ranch (first you need to buy stalls).
You have just caught a chocobo!
The Chocobo Ranch