usually you have to pull it it out where it's tucked in around the edges, or stapled or tacked around the edges if there's garnish molding that you can remove. Then find the bows, and pull them out at one end, then the other end.
Remove it to reuse it? I can take some photos of my '50 Fleetline that came with the headliner missing if that is of some help.
Take out the garnish molding and youll see where its stapled ( or cemented or both) in. Yank it loose from there. Around the doors where its tucked in cut it with a razor blade to release it cause you aint gonna use it again. Then you can get to the bows, usually then you can swing the bows forward or backward so they fall, then pop them out of the holes. The center bow may be held in by prongs that on the roof support that usuall holds the dome light, Bend them back with a screwdriver to release the bow, then take the whole thing out in one piece. If you take the bows out of the old headliner label them 1,2,3 etc. front to back so that if they can be used again the trimmer doesnt have to figure out which one was in which hole. SAVE THE RETAINER STRIP that the headliner was tucked in to around the doots. LEAVE IN any tack strips that the headliner was stapled to that was around window , door opening etc. Good Luck