This is really basic stuff that you can find almost anywhere. Just go to
Gamefaqs.com. Look up Playstation 1 and then FF7 using the platform jumper. The walkthrough Chocobo Manefisto or something like that will help.
If you can't find it there then I will tell you in a short way. Thought it would be faster to look it up. To get River and/or Mountain Chocobo you will need Great and Good Chocobos. You can get good Chocobos at the tracks near the Gold Saucer and great ones in the Mideel area. Good chocobos will have fish like looking creatuers appear with them. Great Chocobos will appear with something called a Spiral that is a light purple. Once you have a great and good chocobo (of opposite sexes) you must race them to S Class and then mate them using a Carob Nut which can be stolen from a red dinosaur like creature that is fought around Bone Village. This will get you either a green or blue chocobo.
NOTE: if this is too confusing please look at gamefaqs.com. I can't say that enoff. Also, DON'T get rid of your Wonderful Chocobo because you;ll need that to get a Gold Chocobo.