Wainscotting. What it is and, how to install it
Okay, first to clear up some misconceptions. Wainscotting is often thought of as vertical bead board applied flat on a wall. While bead board is the most common wainscotting, there are many kinds.
Anything that fills the space between the base moulding and chair rail is wainscotting (even if it's wallpaper etc). Other common types of wainscotting are shadow boxes, and raised panels. The space between the chair rail and ceiling (or cornice) is referred to as the dado. While this is a common joinery term, the meaning is different where wainscotting is concerned.
Many people make the same mistakes when installing wainscotting. The most common is just running the base moulding along the floor. The base must be scribed into the floor so that it's level all around. Without doing this, all of your cuts will have to be slightly out of square, and the chair rail will really show how out of level it is. This will show up even more with shadow boxes. Sidebar: when making your shadow boxes, assemble them before they go on the wall. I like to assemble them at least several hours before installing them. This gives the glue plenty of time to dry (yes, glue EVERY joint). Also, glue everything that you apply to the wall. I like a polyurethane glue best. I use Titebond wood glue exclusively for mitres and joinery.
Another huge mistake people make, at least when using bead board, is not priming everything front and back before installing it. Wood shrinks and expands widthwise, so if the tongue and groove or shiplap aren't pre-primed, raw wood will become visible. Back priming lessens the tendency for the wood to shrink and expand. Also, blind nail the bead board. Blind nailing (in this case) would be nailing into the tongue or groove. This means there's no prep for nail holes before painting.
When using flat stock as base moulding, be sure to mortise the top. The lip created by the mortise will hide the joints. If this isn't done those joints will have to be caulked. This makes a mess when using anything with a quirk or detail. The same holds true for chair rail.
Another problem that can present itself is having sufficient material to nail the pieces to. One thing that I've done in the past, and recommend, is to remove the drywall only in the area that the wainscotting will be applied, then use a 1/2 plywood in its place. I prefer this to framing between the studs and such.
Okay, where pre finished material is to be used, you won't want to nail much. Blind nailing is fine, but not always an option. The product that I always use in this case is Loctite Power Grab. It's a high-tack glue that adheres instantly. The material can be repositioned for some time, though, unlike a contact cement (which I almost never use for woodworking). Save it for your formica work.