As I go to a nude beach just about every weekend throughout the year, this is an easy one to answer. I and many others get naked straight away once out of the clothed area, but this is Australia I'm talking about. So I will walk along the beach naked until I find my spot for the day. Likewise, I don't cover up at the end of the day when I'm leaving until I get near the carpark - which is also shared with a clothed beach.
As for what I wear to the nude beach, shorts with no underwear, rash shirt, baseball cap, and sandals. Given that Australia is the skin cancer capital of the world and I have fair skin, cap stays on, and when the sun is strong or in winter, so does the rash shirt.