Do you have any tips for composting in a very wet, semi-tropical climate?

I live in Louisiana, and my mother's compost piles always seemed to get way too wet during the rainy season. She would put leaves in there to aerate, but then they would always get wet and stick together, effectively making a slimey seal around the contents of the pile. I am about to make my own diy compost bin (out of a plastic trash barrel, in an attempt to keep it dry and also combat the rat problem here.) Can you give me any tips to keep me from turning into my mother? Thank you.