Any good auto store sales spray on adhesive that is used for
upholstery etc. But to do your headliner right you should remove it
from the car. Anything short of this will be a mess and will never
look right.

Take it from someone who knows!

Not lots of fun. Anyway, first get a replacement headliner kit OR fabric
and GOOD headliner adhesive (3M is about the best). The reason the
headliner fell is that the thin foam on the back of the original has
failed. To replace it you need to remove ALL the trim holding the
headliner in place, Then pull the headliner out. Once out remove all the
old fabric and using a stiff brush scrub all of the foam that is on the
backer board off. Then cut the new fabric so it is a bit oversized and
trial fit it to the backer board. Once your satisfied with the fit use a
couple of small pins to secure the new fabric on the centerline of the
backer board. Now you can spray the adhesive on the fabric and the
backer board, work from the center out and make sure not to leave
bubbles or creases in the material. Finish one side and then remove the
pins and do the rest. Let it set for a few hours for the glue to set and
then trim the edges and any inner holes too about 2" all the way around.
Now go around the outer edge and any inner holes (lights and such) and
make sure the fabric will fold back easily, cut darts in areas needed.
Then spray on adhesive and fold the edges back (secure with clothespins
or other weak clamp) once it sets for about a day you can reinstall it.

Steve Williams

3M Trim Adhesive works well.  But first, you will need to remove the
headliner, strip off the fabric, and get rid of the foam, which
deteriorates and crumbles.  That is the root cause of the fabric coming
loose.  If you don't do the whole job, may as well do nothing because
the rest of it will fall off soon.