Lining trunk with smooth material?

Seperate it from the foam sound-dampening, then use vinyl.  Try and get the vinyl that stretches.  will make lining the curves of your trunk VERY easy!  Ide say spray adhesive, but that probally wont work over the stock sound damnpening so if you figure out a way to put it on there, or just get new sound-dampening, then youlle have to lose the dampening, and the vinyl will stick no problem to the trunk.

If you do use spray adhesive, remember to spray it on both materials, let it tack up alittle bit (where if you touch it, it will stick to your finger and pull like marshmellow) then attatch the two together.  Without letting it tack up first, it will make you tired from holding it up there.  Good Luck!!

For this one, it may be a bit tricky... Get your vinyl from www.yourautotrim.com that stuff works really well. second for your adhesive, I would use headliner spray specifically for this install.

To get vinyl to flex properly, you are going to need a hair dryer and make sure the area you are working in is 70* F or higher. gently heat the area the needs to flex and spray it while it is still warm. then spray the panel you are applying the vinyl to. let sit for about 30 seconds - 1 minute (read the adhesives directions) then apply. Make sure you keep the vinyl warm as you apply it, but don't let it get too hot. hold in place for additional minute or so and that should hold it. The heat will make the vinyl very easy to work with and give it a little extra stretch in it. When everything is cooled down and cured (most adhesives fully cure and bond after 48 hours) go over it lightly with ArmorAll or something to help restore anything the vinyl may have lost during installation.

I haven't looked in the trunk of the '06 civic, but if it is like most cars, the carpet in there is a very stiff short pile carpeting. It will be more like pressed fibers. This may work right over the carpet, but I would find a piece from like a junkyard or something and test it on that first.