Melon Farming is similar to Pumpkin farming, as the stem itself does not yield the Melon, but the block is formed next to the stem when it is ready. A Melon can thusly grow in any of the four adjacent squares to the stem.
9 Melon Slices => 1 Melon Block
1 Melon Slice => 1 Melon Seeds
When broken, Melon blocks only yield 3-7 Melon Slices in contrast to the 9 required to Craft it.