Measure the horizontal length of the beam where you will be building the wall. Cut two pieces of 2-by-4 to this length. These two pieces of 2-by-4 are the top and bottom plates of your wall.
Measure the vertical distance between the basement floor and the underside of the beam. Subtract 3 inches from this measurement. This is the length of the studs of your wall.
Measure along the length of the top and bottom plates and mark off every 16 inches. Count the number of marks to determine how many studs you will need. Cut this number of studs to the length you determined in Step 2.
Lay out the wall on the floor. Lay the studs out parallel to each other, separated by 16 inches. Lay the plates perpendicular to the studs and pressing against the ends of the studs.
Assemble the wall by driving two 3-inch-long screws through the faces of the plates and into the ends of each stud.
Check the wall for squareness by running a measuring tape from one corner to the diagonally opposite corner. Note this measurement, then check the opposite diagonal. These two measurements should be the same. If they're not, press or hammer on one of the corners of the longer measurement until you have knocked the wall square and the measurements are the same.
Stand the wall up and position its top plate underneath the center of the beam.
Check that the wall is vertical by holding a 4-foot level up against the sides of the studs.
Secure the wall to the underside of the beam by driving 3-inch-long screws up through the top plate and into the beam.