It's much better to recover your headliner if you remove the old material and foam underneath. To do this, pull the old material off, revealing the foam padding. This is the stuff that deteriorates and causes sagging of the headliner. To remove ALL of the foam, soak a rag with lacquer thinner and wipe until it's gone. Do not leave this soaked rag on the cardboard or damage may result. Once done and allowed to dry, the cardboard will be fresh, clean and ready for your next step. During this process, do not kneel of press onto the cardboard with any type of weight. This will indent the cardboard and all of these indents will be visible after you're done!
Apply adhesive to the cardboard (aerosol spray cans of headliner adhesive can be purchased at any good auto parts store). Use it liberally. Next, lay your new material onto the cardboard (be careful to avoid creases as much as possible) and use a rolling pin to help you smooth out the air pockets and creases. Once done, use a sharp utility blade/razor blade to trim it to the cardboard's dimensions. Good luck!
