Measure out the dimensions of your loft; determine the desired width, length and height.
Cut the 2-by-4s into lengths to make up the frame and at least one cross-member beam. Similarly, cut the 4-by-4s into posts at the desired height.
Construct the frame, placing the ends of the shorter beams along the tops of the longer beams and screwing them into place with two long screws. Center the cross-member beam within the frame and screw it into place with two screws per end. Cut your plywood into appropriate-sized pieces to cover the top of the frame. Screw the plywood to the frame by sufficiently spacing screws, approximately one every 12 inches, along the perimeter of the frame and across the cross-member beam.
Raise the platform and secure the bottom with 4-by-4 posts. Place the posts against the interior corners of the frame and secure them with lag screws going through the frame into the posts (one per side). Place the posts into the corners created by the frame and the cross-member beam and secure them with lag screws.
Place the loft where it's desired and, if possible, secure the sides to the walls of the room.