what is the process called where you put plastic over a picture or document to preserve it?

laminating normally means on laminating machine but it also means:

A laminate is a material that can be constructed by uniting two or more layers of material together. The process of creating a laminate is lamination, which in common parlance refers to the placing of something between layers of plastic and gluing them with heat and/or pressure, usually with an adhesive. However, in electrical engineering, lamination is a construction technique used to reduce unwanted heating effects due to eddy currents in components, such as the magnetic cores of transformers

Laminating will suffice.

If the picture if fairly large, the process to do this and not get wrinkles or creases is to cut a laminate plastic and lay it sticky-side up, and 'roll-press' the picture down onto the laminate surface. Trim the edges, etc.

If the document is old, valuable, fragile or very important it might be better to take the picture to a professional photographer's shop and inquire if they do lamination. They likely would have the proper heat and roller equipment to do the job the best way. Laminating will not increase the value of an antique image, likely it will have a negative effect upon the value and it is irreversible once done.

Laminate

Laminating

laminating