Mix a solution of TSP and warm water and thoroughly clean the tile. TSP is a strong detergent that will remove soap and grease and will de-gloss the tiles so the adhesive will stick.
Cut three or four braces from 2-by 2-inch lumber that extend all the way across the floor from the wall opposite the one you are wainscoting. They should be 1/2-inch shorter than the distance between the walls. Make a notch in the center of each one with a circular saw by cutting across the wood once or twice. The depth of the saw blade should be about 1/4 the thickness of the wood.
Measure and cut the wainscoting with a circular saw and set it in place. Check the top edge with a level to be sure it is perfectly horizontal, then mark its position with a pencil. Remove it and lay it on the floor with the back side facing up.
Cut off the tip of a tube of Liquid Nails with a utility knife and puncture the seal with a nail. Put the tube in a caulk gun and spread a bead of adhesive around the edges of the wood. When the edges are done, lay beads about 4 to 6 inches apart from one end of the sheet to the other, covering the whole interior of the sheet.
Set the wainscot in place against the wall and place scrap pieces of 1/4-inch plywood about 1 foot square at equidistant points on the bottom. Lower the 2-by-2 braces so they wedge against the plywood and the opposite wall. The notches on the braces should be facing up.
Measure the distance between one of the notches and a point about 6 inches from the top of the wainscot and cut a piece of 2-by-2 lumber to that length. Cut as many pieces in this way as you have braces on the floor.
Hold a piece of scrap plywood against the wainscoting, place one of the pieces you just cut into the notch on the nearest floor brace and wedge the other end against the plywood. Tap the end of the 2-by-2 down with a hammer to make sure it is firmly in place.
Leave the braces in place overnight to give the glue time to set. Remove them and set the trim by spreading Liquid Nails on the edge that goes against the wall, setting it in place and taping it to the wall with duct tape to give the glue time to dry.