Either freeze fresh, soft cheeses, such as mozzarella and goat cheese, in their original packaging, or wrap them tightly in plastic wrap and put that in a zipper-type storage bag before tossing it in the freezer. They should be eaten within about two months, and should be thawed in the refrigerator. Since I’m going to use some mozzarella now and have plenty left over, I’ll freeze it in a zipper storage bag…maybe split it up into two or three small plastic bags.
Ricotta cheese cannot be frozen very successfully. Mascarpone can be frozen, but it may separate or shatter when defrosted. It can be re-emulsified, though, by whipping it vigorously with a wire whisk while it is still very cold.