In Farmville, there is a way to breed sheep and rams now since the English Countryside update.
First, you’ll need to purchase the Sheep Pen which costs 5000 coins. Place the Sheep Pen on your farm, and get parts to build it. You’ll need ten Wooden Boards, then Nails, and ten Bricks to complete it. Once it’s complete you’ll get a ram named Brutus to help you start breeding.
If you havent’ received any ewes (female sheep) as gifts from friends, then you can purchase one from the market for 700 coins.
At that point, breeding is fairly simple. Place your ewes and rams into the pen, open the pen, and click on them to breed them. By default it takes 24 hours to breed a par, and it only has a 50% chance of success.
Each Love Potion you add reduces the time, and increases the chances of success. Using 5 Love Potions will make breeding instant, and will give you 100% chance of success, so try to get as many Love Potions as you can if you’re really into breeding.
That’s all there is to it. As far as colors and patterns, a lot of that is random, so keep breeding and trying different combinations for different colors and patterns.