I like to peel the melon before cutting it. Turn the melon on its side so that the stem end can be cut vertically. Slice about 1/8 – 1/4 inch. This should be just enough to cut past the darker green rind. Turn the melon around and cut the other end.
Place one of the cut sides on the cutting board and slice down the side of the melon turning about 1/8 turn after each cut. Cut thin enough slices to remove the rind and the dark green inner layer but not too much melon.
Slice the melon in half and remove the seeds. I usually wait to slice the melon further and store the melon as halves or quarters.