I've used a spray adhesive such as 3M Super 77, available at big box and local hardware stores. A light coat on both surfaces per the directions on the can gives a nice smooth, permanent bond between paper and plastic.
A second vote for spray adhesive, also consider Elmer's spray adhesive. Spray gives a very even surface coat that resists warping and peeling, but most of all won't "bleed" through the paper as other glues do.
Mostly, I use Aileen's Tacky Glue. It's thick and won't soak through the paper, like white glue. That's important, because if I've printed a pattern on the paper with my computer, thin glues will cause it to run. For a very visible surface, I use cardstock, which is stiff enough that it does not ripple even if the glue is a bit uneven. Inside structures, plain paper is fine.
Thanks all. I don't have any Aileen's handy, but would swear I used to have a can of that spray around here, somewhere...
If you go to a craft store, like Michaels, they have spray adhesives for just this application. I know because I've borrowed my wife's a few times. I'll ask her when I get home to see what the name brand is.
Depending on the application but I have used solvent type cement like Tenax. I put the paper in position over the styrene where I want it and brush the solvent over the top of the paper. It soaks through and into the styrene dissolving the top surface allowing it to be wicked up into the paper fiber with a little pressure from above. Dries quickly and leaves a permanent bond. Of course if there is something printed on the paper it may dissolve too. So another method would probably be better for that.
I don't use a lot of solvent, just enough to soak through the paper. If it is thin paper and .03" styrene, should not be a problem. Most of the solvent evaporates before it soaks too far into the styrene. I use this technique for gluing cut paper shingle strips onto a styrene roof.
