Once you can start using the Chocobo Ranch for your own Chocobos. You will need specific nuts in order to breed the special chocobos you need to further breed into a Gold Chocobo.
If my memory serves me correctly, you can't utilize the ranch's services until sometime in Disc 2. I just cannot recall exactly when.
You will want to raise all of the chocobos you use in this breeding to S rank (at the Gold Saucer racing). S rank have a much higher probability of producing the colored offspring you are looking for. Also, just so you know, the breeding will look like this: 2 Normal Chocobos > 1 Mountain Chocobo (Green) and 1 River Chocobo (Blue) > 1 Mountain and River Chocobo (Black) with 1 Normal Chocobo > Sea Chocobo (Gold)
To add to the equation, the normal chocobos have to be of a certain "type", between bad, poor, mediocre, good, great, and wonderful (there might be others as well). This can be checked with Choco Billy once the chocobo is caught and delivered to the ranch. It might seem like you would want only "wonderful" chocobos in order to breed the special ones, but I remember that this was not the case. Certain areas have different specific "types". If you aren't able to get a great or wonderful chocobo from tracks in one area, try moving to a set of tracks in a different area. Obviously, having access to the airship makes this all much easier and faster, but I think you can get the Gold Chocobo before you get the airship. Like I said, this is all off of memory at the moment.