Turn off the oil-fired water heater. Open the service hatch on the oil burner with the screwdriver. Clean off the electrode, the little metal rod near the burner, with sandpaper to remove any rust or other buildup.
Lift the old oil filter from the filter housing above the oil tank. Place a new filter in its place. If the oil tank itself is dirty, dump the old oil into a bucket and pour ½ cup of clean oil into the tank. Wipe the tank down with a cloth and the clean oil. Pour out any leftover oil and fill the tank with clean oil.
Brush out the oil burner's flue with a chimney brush.
Connect a hose to the drain valve at the base of the hot water tank. Place the hose near a drain and open the valve to drain the tank of water. Scrub the inside of the tank with a brush through the hand hole, if present. Rinse the tank, then fill the tank with fresh water.