Please credit Sketchy77 from TrueAchievements.com for the following solution:
This trophy can be easily unlocked in the tutorial area.
After completing/skipping the tutorial, make sure you have a crafting station, and head up the stairs, you'll see a chest with a bow in it.
Now head into the building on your left with the anvil above it. Open the chest, take out a pickaxe, mine 7 nearby cobblestone blocks.
Now exit the building, and go left and straight until you see stairs leading into an underground area. There is a picture frame of redstone on the side of the entrance. Break it.
Now plop down your crafting table, go the the mechanisms tab, and make your dispenser.