Try toothpaste first to remove the tiniest of scratches. Toothpaste is a very mild abrasive that will sometimes work when you rub it in with a very soft cloth. Dab some toothpaste, about the size of a pea, on a soft rag. Work in a circular motion on top of the scratch. Wipe off the toothpaste, using a clean, damp rag. If the scratch is still there, repeat the process of rubbing in the toothpaste.
Rouge is a paste or powder product that you rub onto the glass to help repair scratches. If you buy the powder form, follow the directions for mixing it with water to make a paste. It comes in different grits. Cerium oxide is the base of the rouge. Start with a higher-grit rouge, just as you would when using sandpaper to sand wood. Rub the rouge into the glass, using a soft pad. Rub off all the rouge before advancing to the next grit size. Work your way up to the finer grits. When using the rouge, keep it moist. Have a spray bottle handy so you can spray it from time to time.
A buffer is a must when trying to remove scratches from glass, especially from car and home windows. Use a cordless drill fitted with a buffer pad, or buy a special buffer. The buffer pads are what you use to apply the rouge to the glass. The buffer allows you to rub the glass at a steady, but fast pace. This allows you to take much less time to repair scratches in your glass than it would if you tried to rub it by hand. Some scratches are too deep to be removed by hand alone. However, do not put too much pressure on the buffer when you are using it. Keep in mind that the glass on home windows is much thinner than automotive glass, and it will break much more easily when you apply pressure.
Once you've remove the scratches, the glass will need polishing. This is the very last step when fixing your glass. Use the cordless drill and some polishing pads in the same way that you buffed out the scratches. As with the buffer, do not apply too much pressure to the glass.