In this Instructable I'm cutting an orange flesh melon in most of the pictures, though a cantaloupe also appears. This technique is pretty much universal, though. As a bonus, you don't really even need a cutting board to do it this way - perfect for picnics, and for avoiding invisible onion or garlic contamination on your cutting board.
Check out the video to see just how quick and easy this is:
Step 1: Choose your melon
First, make sure it's actually melon season in your area, as imported melons will almost certainly be sub-par. Melons like hot weather, so melon season usually starts mid-summer, and continues through early fall, though times may vary in your region.
Second, make sure the melon smells good! Give it a sniff: it should smell floral and melony, particularly at the end where the flower bud used to be (the spot opposite the stem end.)
Third, give it a light shake. In cantaloupes and some types of honeydew, the seeds loosen up enough as the melons ripen that they'll rattle around a bit inside when the melon is ready to eat.
If the melon isn't quite at peak ripeness, leave it on the counter so it can ripen a bit more, then put it in the fridge to arrest further ripening. (This is only going to help so much; a completely green melon shipped across the world will never truly ripen.) Bonus: in hot weather, fridging the melons means they're nice and cold when you're ready to eat them. The perfect summer snack!
Step 2: Cut in half
Be sure to wash your melon thoroughly before cutting, so you don't carry any surface bacteria into the edible melon flesh. (Thanks to thematthatter for the reminder!)