Look in the Yellow Pages under Photography Studios, find one that says "Old Photos Restored". They can use a computer reproduction of your photo to add missing parts, highlight, shade, you name it. You'll swear the photo was made yesterday!
If it is an oil painting, a pastel drawing, pen and ink, or any kind of art (not a photo) you can look in the yellow pages under Fine art or Art restoration. You can also contact the nearest good museum and ask who they use? Or if it is not of great value, you can go to your local frame shop, some have artists, who can do minor repairs. (A major rip or tear in a painting CAN be fixed! Never throw out old artwork without checking with an expert. Also I'm a bit in disagreement with the answer above regarding photos. Many old photos may also be quite valuable , so yes, it's a good idea to have a clean copy made , but that damaged original, if it is by a known photographer or is of someone very important (for instance it might be by Mathew Brady and a picture of a famous General) it can most likely be restored unless the damage is too severe, so get a professional opinion! Restoration for works on paper is a specialty, even more difficult than paintings , because of the fragile nature of paper. Photos on canvas or paintings on canvas can be restored in a number of ways, but a tearing requires reweaving (literally weaving the fibers back together). The other way a tear is repaired is by relining where the whole painting is removed an relaid onto new canvas or linen.