After washing the green papaya, peel off the skin using a carrot peeler (or a knife will do as well). You can then either use a cheese grater to shave the papaya, or you can do it the traditional way and hack at the papaya with your knife until there are numerous vertical cuts, then shave off the top layer into thin slivers, and repeat. I like the traditional method as you get bigger, un-even, pieces of green papaya. Cut enough green papaya to have a big handful worth for this recipe.