Lay the sheet of acrylic on a flat and steady surface. Set the polycarbonate sheet on top and verify it is not larger than the acrylic. It must be smaller so it can be attached to the acrylic because the polycarbonate is lighter and will stick better.
Pull the plastic covering off both sheets. Grab the plastic on the corner of both sides of the polycarbonate sheet and pull it off by hand. Repeat the process for the plastic protecting the acrylic.
Open a small can of acrylic glue. Remove the polycarbonate from the acrylic. Dip a small brush into the glue and cover the brush with the glue. Spread out the glue, beginning in the center of the sheet. Work out from there and dip the brush back into the glue when necessary.
Sweep the brush over the entire surface of the polycarbonate until the center is covered with a layer of glue. Work toward the edges and keep the glue at least 2 inches from the edge on each side to prevent the glue from squirting out when the sheets are stuck together.
Place the sheet of polycarbonate on top of the acrylic and carefully press it down into place. Run your hands over the entire area and push down firmly on the polycarbonate. Wait five minutes so the two can adhere together and pull up gently on the polycarbonate to verify they are securely attached.