A scuffed or scratched windshield is not only unsightly, it's dangerous. Being able to see clearly out of your car's windshield is crucial to avoiding accidents, so it's important to take care of scuffs and scratches as soon as they happen.
First of all, make sure it's a scuff mark or scratch and not just dirt. Wash the windshield gently but thoroughly with soap and water, and if necessary, use an ordinary razor blade on an angle to remove any sap or sticky material. If you determine that the mark is indeed a scratch and it's fairly deep, you may need to take the car to a professional. If the mark is a crack, it will simply keep expanding until you have no choice but to replace the windshield. If you find you need to take the car to a professional, check with your car's warranty to see whether such service is covered.
Many scuff marks and scratches result from faulty or ageing windshield wipers scraping across the glass. You can try any one of a number of abrasive "recipes" and see whether it helps remove the mark. One of the products most recommended by mechanics is cerium oxide, an orange powder you can find in auto stores or online. Wet a soft cloth or sponge and dip it in the oxide so that you make a paste on the cloth. Then rub the cloth in small circles, using pressure over the scuff marks, but keep checking your work so that you don't overdo it.
Buy some jeweller's rouge (iron oxide) for removing the scuff mark. It can be found in department stores, hardware stores, hobby shops or jewellery supply stores. Mix 28.4gr of iron oxide into a paste with 28.4gr glycerine and 28.4gr water. Put a small amount on a cloth and rub it onto the scratches, washing off with clear water from time to time to check your progress.
If you have difficulty locating cerium oxide or jeweller's rouge, try ultra-fine steel wool (0000 grade) and buff very gently followed by a glass scratch remover product from an auto supply store.
Other abrasives you can find in your local grocery store may also work well. Bon Ami and Bar Keepers Friend are two lightly-abrasive products that are safe to use on most surfaces. Just as with the cerium oxide, take a little on a wet cloth and buff the scratch or scuff mark until it's gone. If you have an electric buffer, you can use that instead of plain elbow grease. Toothpaste (not the gel kind) is another very fine abrasive that can be used with a cloth to remove marks.
Many auto supply stores sell windshield repair kits or windshield scratch or scruff remover kits that usually consist of a special glass-polishing wheel or pad and different grades of pumice powder. These kits come with full instructions, are easy to use and won't damage or distort the glass.
If all else fails, or if it appears that your windshield damage is worse than you initially thought, take the car to an auto glass shop. There they will use a clear epoxy and careful buffing, or something similar, to fix the damage, and in most cases, it's a relatively easy and inexpensive job.