First peel the green papaya, then use the largest grater you have (like what you would use to make scalloped potatoes) and grate the green fruit, rotating it as you go to avoid hitting the inner seeds. If you don't have a grater, try the second method, which is the one they use in Thailand. Use a large, sharp knife. First deeply score the flesh, then run your knife just under the surface to release beautiful shreds (for a visual tour on how to do this, see my : how to make green papaya salad