Generally, you need a "license" when you need special permission -- like a license to practice law or medicine. There's usually no special "license" needed for graphic or web design. However, if you are doing your freelance work under a name other than your own -- for example, "Robin Smith Graphics" (instead of just "Robin Smith"), you will have to file a business certificate with the local county clerk.

Confirm with an attorney in your state to make sure you're following the rules properly.