They probably aren't going to remove the screen at all. What most shops do, and what I did on my Camaro's headliner, is to leave the headliner up and tuck the egdes.
You obviously mask off anything you don't want to get glue on near the spray area, blue painters tape works very well.
Trim the new material just slightly larger than the area you are covering (so you can tuck the edge under the trim).
Spray both the screen and the material you are using to cover it (usually foam backed felt/cloth) with yellow upholstery glue (you can use 3M super XX if you don't have access to other stuff, Super 77 works OK).
You let the glue set for 15mins-1hr depending on which glue you used, so it's almost completely dry. If you touch it and its very sticky, it's not dry enough yet.
Place the new material in the center, firmly and slowly work outwards.
Once you're at the edges, gently tuck the new material under the trim with a dull butter knife (or equivalent). If you have left too much material, trim with a very sharp exact-o knife.
If you get any glue on the plastic trim, just clean off with mineral spirits and a cloth.
I would try this first, and if it doean't work for you, all you're out is about $12 in supplies
then you can take it and have them do it! Good luck.
Chas.
