How to fix an old photo, by what went wrong with it
Most advice about restoring old photographs treats damage as one problem. It is not. A torn print and a faded one have almost nothing in common, and the fix that works on one does nothing for the other.
Work out which kind of damage you are looking at first. That decides whether this takes two minutes, whether it is worth paying a person, and occasionally whether it is worth doing at all.
Tears, creases and missing corners
Physical damage is the most recoverable kind, because the information is usually still there on both sides of the tear. Software reconstructs the missing line by reading what surrounds it.
The exception is a tear straight through a face. Reconstruction there is invention: the result may look convincing while being wrong about the one thing you care about. If the print is important, this is where a human retoucher genuinely earns the fee.
Water damage and mould
Water damage comes in two stages, and only the second is a scanning problem. While the print is still damp or stuck to glass or to another print, it is a handling problem, and pulling it apart is how the emulsion comes off.
Once it is dry and separated, the staining and blooming that remain are recoverable to a surprising degree, because the underlying image is usually intact beneath the discolouration.
Fading and colour shifts
Colour prints from the 1960s to the 1980s tend to drift towards red or magenta as the dye layers break down at different rates. This is the most common thing people mean when they say a photo is ruined, and it is also the most reliably fixable, because the shift is systematic rather than random.
Silvering, and when to stop
A mirror-like metallic sheen on a black and white print is silvering, where the silver in the emulsion has migrated to the surface. It is a physical change to the object rather than a change to the image, so a straight-on scan will capture it as glare.
Photographing the print at a slight angle, or scanning it, usually gets past most of it. Heavy silvering across a face is one of the few cases where the honest answer is that a copy will never be as good as the original, and the original should be stored properly rather than restored.
Questions
Can a badly damaged photo really be restored?
Usually, if the damage is around the subject rather than through it. Restoration reconstructs from surrounding detail, so a torn corner is straightforward while a tear through a face is guesswork, however convincing the result looks.
Do I need to scan the photo first?
A phone photo in even, indirect light is enough for most prints. Scanning helps most with silvered or glossy prints where reflections are the problem.