Measure the sides of the beam and add 3 inches to it. Cut four 2-by-4s to match this measurement.
Place two of the boards from Step 1 on the floor on opposite sides of the wood beam. Set them so 1 1/2 inches of the boards stick out on each side of the beam. This accounts for the extra 3 inches you added to the measurement. One and 1/2 inches is the actual width of a 2-by-4, and this will allow you to fit more boards flush in between these two.
Drill the boards to the floor joists with 3-inch screws.
Hold a plumb line from the ceiling until it touches the outside edges of the boards you installed at the bottom. Check both ends and the side of the boards. Mark the ceiling to indicate where the plumb line is at these points. This is where the top boards, or top frame plates, need to go so the box frame is straight. Measure the marks to determine if you need to trim the boards in any way. Use a circular saw to trim them if necessary.
Place the top boards on the ceiling and attach them to the joists with 3-inch screws.
Measure the opening between the two bottom plates on the other two sides of the wood beam. Cut 2-by-4 boards to match these measurements. Install them in the gaps between the first two bottom plate boards. Repeat the process with the top plates, but check the top plate locations as before with a plumb line.
Measure the distance between the top and bottom plates. Transfer the measurement to 2-by-4s and cut out four boards.
Slide the boards in between the top and bottom plates at the four corners to create studs.
Drill 3-inch screws at an angle through the ends of the stud and into the top and bottom plates.
Measure two opposite sides and transfer the measurements to drywall. Mark the drywall with lines for cutting.
Score the lines with a utility knife, and then go back over it to cut it out.
Place the drywall up to the sides and attach it to the wood frame with drywall screws. Set screws every 7 inches.
Measure out the space on the other two sides, and include the edges of the first two pieces of drywall. Transfer the measurements and cut out more drywall.
Set the drywall in place and screw it into the top and bottom plates as well as the studs.
Measure the height of the boxed in beam, and cut metal drywall corner protectors to this length. Use metal snips to cut the strips.
Place the corner strips up to each of the four corners and screw them in with drywall screws. Cover the corners with drywall compound using a 4-inch taping knife. Use a thin coat and let it dry for a day.
Sand the compound smooth the next day and apply a wider coat with a 6-inch taping knife. Taper the edges of the compound as you move away from the corners. Let it dry another day, and then sand again.