Yes, you do need a license to fish. Learn about fishing licenses in SC at the Department of Natural Resources, where you can get licenses online. But if you're already at the beach and want one right away, visit Pawley's Island Outdoors. You will need a license for catching crabs only if you use more than two pots, but you can learn more at DNR.
Equipment
You can find equipment at many places on Highway 17 and in Georgetown. For crabbing, the easiest place is Pawleys Island Supplies, at the corner of the North Causeway.