Check out these links on YouTube. They are the best headliner repair videos I have seen and go into enough details to do it yourself. They also tell you why they fall down and why just sticking them with glue will never last long.
Fix a headliner the correct way:
https://youtu.be/kZ_bICRvh-Y
Volvo S40, sagging headliner and sunroof repair:
https://youtu.be/xCxRMnw_Uok
How to remove a saloon car headliner:
https://youtu.be/5qv-LrJAULo