Watermelon and honeydew
To eat these big things with the proper etiquette, cut the fruit into large slices and then carve the edible bits (minus the skin, of course) out into manageable sized pieces which can be eaten with a fork. Seeds should either be picked out prior to picking up the piece with your fork or spit out into your hand and placed into your plate (not spat out, of course). Informally, just take the large slices and launch into them like a monkey would.