The walls of your shed do not need to be finished, but they should be insulated to protect against the change in temperature. Shed wall insulation can be accomplished with foam insulation boards attached directly to the interior of the shed walls, or you can put exterior foam board insulation under the shed siding.
The ceiling insulation for a shed can be approached in much the same way that you would insulate the roof of your home. You could use fiberglass insulation that comes in rolls and is installed with a staple gun, or you could apply blown-in insulation directly to the roofing deck from inside the shed.
According to the Secrets of Shed Building website, a common type of shed floor is a wooden one. A concrete shed floor can resist the cold, but wooden floor boards could use help in maintaining the shed's temperature. One way to help a wooden shed floor resist changes in temperature is to install fiberglass rolled roofing insulation under the shed floorboards. The fiberglass is waterproof and will be able to withstand exposure to moisture.
Wind and moisture can get into a shed through a poorly insulated doorway or window opening. When you insulate your shed, be sure to caulk around the windows and doors. You can also use expandable insulation from a can around the doorways and window openings to help further protect your shed.