Instructions
Walk south from your town to the beach and look for a coconut washed up on the shore. Coconuts appear randomly on the beach once a week. Try searching on the beach a few times a day to maximize your chances of finding a coconut.
Pick up the coconut on the beach by pressing "B" on the Nintendo DS or the Wii remote.
Grab your shovel by selecting it from your inventory and walk up to the grass next to the sand on the beach.
Position yourself about nine paces off the beach and use your shovel to dig a hole in the grass. Drop the coconut into the hole and use your shovel to cover the coconut with dirt.
Check the spot where you planted the coconut in a few days. Hopefully, the coconut has sprouted into a coconut tree bearing two coconuts. If not, continue looking for coconuts on the beach and try again.