First of all, it's not clear what kind of damage you're talking about. The words "door ding" usually describe metal that has been dented in one particular spot. If the metal has indeed been dented, I suggest you seek the services of a paintless dent repair specialist in your area. If, OTOH, it is just a smear mark and the metal is still smooth, read on.
If it is just a smear mark, then you will want to follow "standard operating procedure" by starting with the mildest materials and procedures. If they don't work, then proceed to more aggressive measures. As follows:
1. If it's just a mark, try washing the car and see if it comes off. Maybe it's just dirt.
2. If that doesn't work, and if it's a black mark like road tar, then you might try a solvent such as a tar remover that you can get at your local auto parts store. If this fixes it, then wash and wax afterwards, and you're done.
3. Next thing to try is a non-abrasive polish, like Zymol HD-Cleanse and/or one of the different makes of detailing clay on the market. This will remove many marks (e.g. tire marks) and oxidation and even light scratches. If this fixes it, then wax afterwards, and you're done.
4. Next thing to try is something that is slightly abrasive, such as Meguiar's #9 Swirl Mark Remover 2.0. This product is particularly good as a first step if the paint has been scuffed (so it's moderately scratched and not totally shiny in the affected area). If this fixes it, then wax afterwards, and you're done.
5. If the mark is still there, then you need to try something significantly more abrasive. At this point you're probably going to be using some sort of rubbing compound or polishing compound, possibly even fine sandpaper. This step is not for the faint-hearted, and while the do-it-yourselfer can try it, you might want to consider turning to a professional (detailer or body shop) at this point. If you do it yourself, follow it up with the Meguiar's #9 Swirl Remover 2.0 to smooth it out, then wax afterwards, and you're done.
