Wash and dry the window.
Squeeze a liberal amount of toothpaste onto your fingertip.
Rub the toothpaste into the scratches on the window glass until they are completely covered.
Wipe off the toothpaste with a soft, clean cloth. Rub in circular motions until all the toothpaste is removed.
Buff the glass with a clean cloth.
Inspect the window glass to see if the scratches are less visible. If they can still be seen, repeat these steps as necessary.