Get a Good or Great Chocobo. Best place is near Mideel the southern most town on the world map. Use a Carob nut to breed them. You get Carob nuts from Red Dragons type things just south of Bone Village. May as well get 3 of them while your at it as thats how many you'll need in total.

Once you have a Green & Blue Chocobo breed them using another Carob nut and you'll get a Black Chocobo. Then you need a Wonderful Chocobo which you get from near Icicle. Breed the Wonderful Chocobo with the Black one using a Zeio nut and you'll have a Gold Chocobo. You can get the Zeio nuts from goblins on a little island to the right of the top continent.

You also need to win Chocobo races at the Gold Saucer with all the Chocobos you catch and breed.

It takes a long time to get a Gold Chocobo but it's worth it.