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.
Nina L. Kaufman, Esq. is an award-winning New York City attorney, edutainer and author. Under her Ask The Business Lawyer brand, she reaches thousands of entrepreneurs and small business owners with her legal services, professional speaking, information products, and LexAppeal weekly ezine. She also writes the Making It Legal blog.