How can paper be glued to cardboard without creating wrinkles? In my projects, I often wish to affix a piece of paper to a more rigid material, like cardboard, and to do so using relatively large sheets of paper (say, around a square foot or two). However, I find that it is very difficult to get the paper to lay flat after placing glue on it.

Are there specific types of adhesives or techniques for applying glue that minimize the amount of wrinkling caused?

I understand that the wrinkles are caused by the paper expanding when it is exposed to moisture. Thus, I've tried to minimize the amount of glue I use, as well as tried letting the paper sit for a bit with the glue before placing in against the other surface to give an opportunity to expand beforehand, but still haven't gotten a good result. I've tried using wallpaper paste, PVA glue, and wood glue for this purpose, but the results seem very similar with each.
Use SprayMount, or similar - it is formulated for exactly this purpose: fixing paper to cardboard.

What you do is place your artwork face down on a piece of newspaper, spray a single, thin coat on the back, then place it onto the cardboard. It dries almost instantly, so there is no wrinkling, while still giving very good, invisible adhesion. There are some varieties which are repositionable/removable too!