Line the entire perimeter of your poster with the craft tape. Keep the tape as close to the edge as possible.
Remove the craft paper backing from about half of the poster. Place the poster on the foam core, aligning one edge to a straight edge of the foam core. Carefully stick down the exposed tape, using your hands to apply pressure.
Remove the rest of the craft paper and stick down from the center out.
Use the straight edge and box cutter to cut off the excess foam core. To cut through foam core, make sure the blade is sharp. Take it slow, and take multiple passes through the material. Think of it as cutting through three layers. First cut the top layer of paper. Then cut through the foam layer. Last, cut through the bottom paper.
Now you have a nicely mounted poster!