Cut the 18-inch hollow door in half vertically with a circular saw or table saw to create two shelves that are 9 inches deep. The cut side will go against the wall when the shelf is finished.
Paint the shelf in the color of your choice. It's easier to paint now than paint after the shelf is in place.
Mark the location of studs on the wall with the aid of a stud finder, then use masking tape or painter's tape to experiment with horizontal placement of the shelf. Take into account the location of the studs when deciding the final location.
Create a level guide for placing the shelf. Use a carpenter's 4-foot level and a pencil to mark the location of the shelf.
Construct your cleat. Measure the inside clearance of the hollow door shelf. The cleat should be the same size as this clearance because the hollow side of the shelf will need to fit on the cleat perfectly. Cut the 2-by-4 stud to the proper size for this. Cut the length of the wood the same size as the length of the hollow door. Check to ensure that the resulting strip of wood fits snugly inside the hollow door.
Drill starter holes and attach the cleat to the wall at the studs with 3 1/2-inch lag screws using a socket wrench.
Remove any cardboard bracing inside the hollow door shelf to a depth of 1 1/2 inches to make room for the cleat. Slip the open side of the hollow door onto the cleat to make sure it fits. Sand where necessary for the closest fit possible.
Remove the shelf and apply carpenter's glue along the bottom inside of the shelf opening and on the top of the cleat. Put the hollow door back onto the cleat, mounting the door smoothly against the wall.
Drive 1-inch brad nails into the back edge of the shelf with the hammer, attaching the shelf to the cleat.