It depends heavily on the type and age of the print. There is no universally safe cleaning method for all photographic prints, and cleaning unidentified older prints is risky.

A cautious approach from the community advice is:

1. Start dry: gently try a soft, absorbent cloth first.
2. Test before doing anything wet: on a less important print or a small edge area, lightly use a damp cotton swab to see whether the image or surface is affected.
3. If the print tolerates moisture, some users report success washing conventional photo-paper prints in water with a tiny amount of mild dish soap, then rinsing and air-drying flat on a towel.

One answer also suggested a glycerol/isopropyl-alcohol mixture for specific older darkroom papers, but that was developed for particular paper types and is not broadly safe advice.

So: for modern, sturdy photo-paper prints, careful testing may let you clean them yourself. For valuable, old, unusual, matte, or unidentified prints, a conservator is the safer choice.