Another task that's within the reach of do-it-yourselfers is windshield scratch repair. But this fix is rather complex — skill is required to do it properly. Read on and decide whether it's a task you want to take on yourself.
First: a scratch is just a surface thing, just as the name implies. A big scratch is one that you can get a fingernail into. In fact, if the scratch is that big, or if it's a long one, that may be the signal that you should leave it to the pros. And if the damage extends all the way through the glass layer, down to the lamination, then it's a crack and can't be fixed by the methods described here.
All the literature and instructions and word-of-mouth information that you'll find will stress that scratch repair is not a thing you can master at the first try. Some go so far as to suggest buying a few beaten-up windshields to practise on! Certainly, don't try fixing your own or a neighbor's windshield as a first attempt (unless, of course, you're leaving town tomorrow!)
The basic theory behind scratch repair is that you gently abrade away the damage while at the same time refilling the cleaned-up area with a glass substitute. The two usual variations on the practice are single-step and multi-step. If you're using the single-step system the polishing/repair compound is applied to the polishing disk; otherwise it's applied through the polishing tool. All systems have a water supply tank and a compressor. It's recommended to use distilled water because it will be free of contaminants, such as grit and chemicals. The water does two things: it carries away the abraded glass and keeps the windshield properly cool: if it heats up it will become distorted, perhaps making things worse. From this it follows that the job is best done out of direct sunlight.
Clean the windshield very carefully and cover the paintwork so that it won't get splattered or otherwise damaged. For a multi- step process (and perhaps for one-step as well) create a dam on the windshield of tape: take 2" tape (such as duct tape); stick one edge on the windshield, about one foot in length vertically; take another strip of the same size and attach it to the first one, sticky side to sticky side, also attached to the windshield; repeat above but horizontally. The purpose is to make the best possible use of the water and to prevent it from spraying all over the place.
The exact sequence of events now depends on the process you're using and the repair kit. Step one will be to select a polishing disk and attach it to the buffing machine. Start up the pump and adjust it properly; gently buff the affected area for an appropriate time; repeat with a different disk if required. All systems require practise and care in getting the timing, the amount of pressure applied by the buffing machine, the amount of water needed, and the area to be ground correct. Once done, no ripples in the glass should be apparent and the scratch should now be invisible. The exact instructions will depend on the repair kit you're using. Make sure to follow them carefully!
When you're done, clean up the windshield, the car, and the tools properly.
These kits can be used for all sorts of glass repair, not just for windshields, so long as the glass is robust enough to stand up to the pressure. However, they won't be any good for acrylic surfaces.