A new backing for a simple picture frame
A replacement backing must fit the frame recess without forcing the picture and glazing together.

Understand what the old backing does
Open the frame over a soft surface and keep the parts in order. Check whether the old backing also carries the stand or hanging hardware. If so, it is more than a loose cover. Thin homemade board does not automatically replace that structural role. Use an appropriate replacement or have the backing renewed professionally.
For a light frame with separate hanging hardware, the old backing can serve as a template if it is not distorted. Also measure the recess itself. The new piece should drop in rather than be forced. Check thickness as well, since retaining clips accommodate only a limited stack.
Measure more than one edge of the old backing. Damp board may have become skewed, and tracing it directly would repeat that error. Compare diagonals and check against the actual recess. Extra size is not extra security: an oversized panel can push the frame joints apart. A loose paper trial establishes the outline first, while the final board thickness is checked separately. Shape and thickness are two different fitting questions.
Match the material to the contents
Clean firm board may suit a changing display made with copies. Photographs and valuable paper originals need appropriate preservation materials; ordinary packaging board may contain unsuitable substances. One added sheet of plain paper does not automatically make an unsuitable backing archival.
Mark a square-cornered rectangle and cut with controlled passes on a suitable mat. Remove loose fibers. Round corners only as much as the recess requires. Large corner cutouts let the backing move and may hold the contents unevenly.
Assemble without excessive pressure
Replace glazing, any spacers, the image and backing according to the intended construction. The contents should lie flat without being forcibly squeezed against the glass. Close the existing retainers only when the thickness fits. Do not repeatedly bend damaged clips until they break.
Stand the frame upright and confirm that the backing stays secure. Movement may indicate too much clearance or missing parts. Do not attach a new hanging cord to cardboard with craft glue alone; the load needs suitable hardware. A decorative backing can carry the date of the image change if that helps track its history. Keep labels away from the photograph itself and preserve any original information separately rather than discarding it with the old board.