Have relatively new headliner but it is coming loose around the edges. What is the best way to glue it back in place?

 

Spray adhesive like you would use under carpets... let it go tacky or it may soak in and stain. Minimal amount on the fabric more on the backing.

 

3M make's a headliner adhesive, usually available in your local auto parts store. PN 38808. Spray it on in two coats, both sides. Let it get to the point of almost being dry to the touch ( it is contact cement). When you move the headliner back into place, it will immediately stick, and you will not be able to re-position it, so be very careful.