You must first have a barn built by Gannon on your farm. Once you do, they will become available for purchase for 4,000G each. An adult sheep can be sheared using a pair of clippers every 3 day. Wool can be sold or turned into yarn. Brushing sheep with the Brush will increase their friendship and their wool quality.
As you increase friendship points with your sheep, the quality of wool will go up. If you win the sheep contest, they will start to produce s-rank wool, and you'll be able to purchase Suffolk Sheep.
If you use a Miracle Potion on a sheep, the sheep must not be sheared for the potion to work. A sheep will give birth in 16 days, and it will take another full 16 days from the birth for a sheep to be full grown. Sheep will live for approximately 5 years if they are properly cared for.