I use 4'x8' sheets of .060" thick styrene, and "prep" the styrene using lacquer thinner (usually applied with a 2" brush) then brush-on gelled contact cement - the lacquer thinner reacts with the plastic to make application of the contact cement much easier.
After brushing the contact cement onto the plywood, I wait until the contact cement on both the plywood and the plastic is dry to the touch, then carefully bring the two surfaces together. (If you're uncertain about getting the piece of plastic properly positioned, cover the contact cement on the plywood using waxed paper, which will allow you to jockey the plastic into place, then carefully withdraw the waxed paper, pressing the plastic into place as the waxed paper is removed.
Wayne
