Install a length of 2-by-4 inch lumber to serve as the top plate for the basement wall. The wood should be cut to the length of the wall you are erecting, then fastened to the floor joists above with a hammer and 3-inch nails. Install a second top plate directly beneath this one and fasten it to the first plate with the hammer and nails.
Lift the wall header into position with the help of an assistant, and use lengths of 2-by-4 wedged between the underside of the header and the floor below to hold it in place. Hammer nails through the header and into the plates above it at an angle. Toenail the edges of the beam into the king studs at each end of the wall opening as well.
Install blocking between the floor joists above the wall header to reinforce the structure. Cut pieces of wood to bridge the gap between the joists attached to the header, and the next one over. Use the same size wood as the joists, and drive nails through the joists and into the ends of the blocking on both sides to hold it in place.