How do you research an old painting?

There is no simple answer. If the painting is signed and if you can work out the name, first try to find out more by using websearches. (Note that many paintings are signed on the back). Also try to work out the genre and period; at the risk of pointing out the obvious, if the painting is signed 'James A. Smith' for example there may be several artists with the this name ...

If the painting is unsigned you will need to get advice from someone with a good knowledge of art history. It may be possible for an art auction house to identify the artist on the basis of a really good photo, or at least make an informed guess. If there is an art museum near you, they may be able to help you.

(Sometimes it is necessary, in the interests of preservation, to have an additional canvas stuck to the back of the original canvas, especially if the original has buckled. If there is a signature on the back, always take a good photograph of it before having it covered up. If you have to have a painting restored get advice on restorers as their competence varies enormously. Find out which restorers are used by an art museum and/or auction houses).