The headliner is one piece of cardboard, the foam/fabric is glued to that. You have to remove all traces of the original foam so the new will stick well and not have lumps in it, although that's usually not too hard to do - a nice wide scraper will do the trick.
The new fabric will have the foam already glued to it, you can buy a 3M product made especially for this, but it's just contact cement. You'll get a more even coating using the spray version rather than trying to brush or roll it on.
Spray both the cardboard and the back of the foam/fabric, let them dry then carefully lower the fabric onto the carboard. Trim around the edges leaving some to tuck in as needed, then reinstall the headliner.
You have to remove pretty much every trim piece on all the pillars to allow the headliner to come out, but they're mostly held in with screws. That takes as much time as the rest of the job. Work carefully and you'll get a great result.
I've done many of these on lots of different cars, it's not that hard but you need a good clean open area to work, and either a flat table to work on the cardboard or a clean place outside with some sheets or cardboard to work off of.
On the second gen cars the headliner is some sort of carpet material (no clue where you'd get it, though I assume certain fabric shops have it). I assumed the first gens have the foam-fabric dave is talking about since you stated it was falling, which is usually the thin fabric comming off of the foam which remains securely glued to the headliner cardboard. Definately no fun scraping it all off but its a must do.
As far as the glue, the fabric store I visited once stocked it... just was 'headliner spray glue'.
Tried 3M regular Super77 or whatever it is which can usually hold damn near anthing, but it wouldnt keep the headliner glued right.
Automotive upolstery shops will have or be able to get pretty much any headliner material you want - but they may be a bit more spendy than a fabric shop. The last time I did one (the wife's Rabbit GTI) I bought the exact matching fabric from the auto upolstery shop and it was about $120. It's been a while since then tho....
You might call around a couple in your area and see what they charge to just replace it - especially if you don't have a good place to work. I had a nice 4' X 8' table in my basement to lay it out on.
Or you could remove the headliner and take it to the shop and have it recovered, then you could just re-install it. Be glad it's not made like my Jag tho, on it the material is simply glued directly to the metal roof. Let me tell you what a fun job that is to replace!
