Things You'll Need. 1  Fresh, ripe papayas. 2  Paper towels. 3  Vegetable peeler or paring knife.  Sharp kitchen 1  knife. Soup spoon.  Rinse the papayas in cold water and pat them dry with a paper 1  towel. Peel the papayas using a vegetable peeler or paring 2  knife. Cut the peeled papayas in half lengthwise.