Peel the melon before you split it in half. Slice off the top and bottom and place it, either cut side down on the cutting board for stability. Then just run the SHARP knife (this is important; a dull knife will tear the flesh of the fruit and is dangerous to use as well) down the sides following the contour of the melon. This is much easier, faster and safer and will prevent you from asking your deity for forgiveness for the profanities you might have used during the process suggested.
If you can, try to use a melon other than boring honeydew or canteloupe (ie. casaba) and for an additional final garnish divide very thin strips of 4 slices of prosciutto amongst the plates. I know. This raises the sodium content but the added dimension of sweet-salty is amazing. I tried it this way and i didn't hate it.
Cheers and Enjoy