Formica is glued to plywood in the manufacturing of kitchen countertops or any time a waterproof surface is needed. Contact cement is used to glue Formica to plywood; wood glue will not work. Contact cement bonds permanently on contact and provides the necessary barrier to prevent moisture from penetrating. Contact cement is waterproof and stays sticky for years but can easily be dissolved with acetone if you ever want to separate the Formica from the plywood.
Lay the plywood and the Formica across two sawhorses.
Spread an even layer of contact cement on both pieces with a small paint brush. Let the cement dry for 20 minutes.
Lay dowel rods across the plywood 3 inches apart with one end of the dowel rods extending out over the edge of the plywood.
Lay the Formica on top the dowel rods. Starting in the middle, and pull the dowel rods out one at a time until the Formica settles evenly on top the plywood.
Tap the plywood lightly with a rubber mallet starting from the middle and working toward the perimeter, tapping over and over again until the Formica is permanently bonded to the plywood.
Don't tap on the edge of the Formica if it extends out past the edge of the plywood. It will break. Always glue up bigger pieces than you need and cut them down with a table saw after they are glued together. Gel formula contact cement is the easiest to use.
Wear breathing protection when working with contact cement. Use only in well-ventilated areas. Turn off all pilot lights in the immediate area. Be careful, contact cement fumes are very volatile.