Is the actual board damaged? If it is just the material and foam that are worn, then you can reuse the original backing board. Remove all the headliner and foam material you can by hand, then go back over what's left of the foam with a stiff bristled brush. Actual headliner material come with a foam backing, but if you want you can use a thin layer of foam, and some light weight vinyl, to get a nice finish.
Remove complete headliner from your stang. Once the board is free of old foam residue, lay the foam (very thin) over the headliner board. Fold half of the material back, and spray the face of the headliner board, as well as the mating surface of the foam. Lay out the foam in a smooth fashion. The you can fold back the other half of the unglued area, and repeat the same step. Applying the light weight vinyl of your choice, will be applied in the same fashion as the foam was, one half at a time. This reduces your chance of wrinkles in the final product.
After the material is in place, you can use a razor blade to trim excess material from the edges of the board, as well as cut the opening for the dome lights. You can trim, and glue these openings for a nice factory style finish. Reinstall in vehicle, and feel proud of your own work.