Decide how large you want the screen to be. Measure and cut the lumber using a tape measure and the miter chop saw to create a frame that size. Set the miter saw at a 45 degree angle, and cut through the two 1 foot by 1 foot pieces of plywood so you have four triangles.
Lay the frame down on the floor. Place the one plywood triangle in each corner. Make sure the grain of the triangle runs perpendicular to the seam in the lumber to increase the strength of the seam once assembled. Screw the triangles to the lumber with the drywall screws and the electric screw gun.
Pick up the frame, and lay down the fabric on the floor. Make sure the fabric is free from wrinkles. Lay the frame on top of the fabric with the triangles facing up. Center the frame inside the fabric. Pull the edges of the fabric around snugly to the back of the frame and staple. Try to pull evenly all the way around the frame to prevent wrinkles from forming in the fabric while stapling. Hammer down any staples that are sticking up. Trim the excess fabric off using a utility knife.
Decide how high you want the TV to stand from the floor. Add one foot to the desired height, and cut pieces from the 2 inch by 4 inch by 8 feet lumber with the miter chop saw at this height. Screw these pieces to the back of the frame to become the legs of the TV at the desired height. Cut two 2 inch by 4 inch by 3 feet support pieces. Screw these pieces into the bottoms of the legs to create T legs with the supports oriented perpendicularly to the screen.
Set the TV up in the chosen location. Place the mirror behind the screen. The mirror should be the same size as the screen and be mounted at the same height as the screen. If the mirror doesn't come with a stand, build another like the one used for the TV.
Mount the projector in front of the screen near the ceiling with the mounting hardware provided with the projector. Aim the projector at the mirror. Turn on the projector and begin the trial and error process of changing the distances between the projector, mirror, and TV to find the appropriate distance ratios needed for the image to fit the screen. Adjust the focus and keystoning on the projector once the distance ratio has been reached.