First buy four stables for starters. If you need money try selling an "all" materia.

Catch chocobos from Midel or gold saucer areas. When you have a male and female from those tracks you need to put them in your stables.

Next you will need to steal a carob nut from Vlakorados near bone village in the green areas not the forests. Better still two or more. You need three altogether.

Next you are ready to breed. You can raise your chances of getting a blue or green chocobo from racing but its not necessary. All you have to do is save, mate the two with a carob nut and if you don't get a rare bird reset and repeat.

One you get a green and blue chocobo of opposite sex its time to mate them. Save in case you don't get the results right. Use another carob nut and you should get a black chocobo.

From there catch a chocobo from the icicle inn area and you should get a wonderful chocobo. mate a wonderful and a black chocobo with a zeio nut and you should get a gold. Zeio nuts can be found on goblin island on the east most part of the map.