Fill small holes along the flooring and roof with silicone caulk. This is an area where small holes are common. Pump the caulk over the hole and then spread it around with a finger while wearing gloves.
Fill larger holes with expandable insulation foam. Shake the can. Hold it upside down and spray the foam into the hole. Let the foam dry until it is hard to the touch. Pare down any excess with a utility knife.
Caulk around windows and doors with a caulking gun. Lay down a 1/4-inch bead of caulk around the exterior edges.
Nail boards over the windows. A broken window is an excellent entrance for a small animal or bird. Place plywood or boards over the window and nail them into the window frame.
Look for any remaining holes to fill. Stand in the shed with the lights off during a sunny day. If you notice any light coming through holes in the walls or roof, fill these holes as well.