Prepare the papaya: Slice off the ends of the green papaya. Using a vegetable peeler, peel the outer skin. Hold the peeled papaya with one hand and tap the papaya with a sharp knife with the other other. You should see shallow knife marks on the papaya. Carefully slice off a layer of the papaya (where you have been tapping), creating green papaya shreds.
Watch this video for the technique. If this method seems a bit dangerous or tiring to you, see the notes above for an alternative shredding method. You only need about 4 1/2 cups of shredded green papaya.