Scrub the glass with a soft bristle brush to dislodge and remove dust and oil.
Wash the glass with a soft sponge soaked in a solution of 25 percent white vinegar and 75 percent water. Rinse with plain water.
Remove remaining dirt with a commercial window cleaner. Dampen a soft sponge with the cleaner and scrub the window side to side in straight strokes from the top down.
Spray stubborn spots with a spray bottle and gently scrape them up and down with a wooden scraper to remove them.
Wet one side of a squeegee blade with water and move it straight across the window from the top down to dry it.
Inspect the window for any remaining scratches. Drag your fingernail across the scratches. If your nail catches, you will not be able to fix the scratches yourself. You will need to call a window repair professional or replace the pane.
Repair small, shallow scratches with a commercial windshield glass repair kit, available at auto parts stores. Apply the solvent and buffing compound to the glass and buff away the scratch according to package directions.