Raise the stud wall and maneuver it into position.
Push wooden shims in between the top plate of the stud wall and the joists at each point where they intersect. Snap off the excess wood of the shims.
Drive nails through the top plate from below, directing the nails through the plate and shim, and into the joist. Use two nails at each intersection.
Measure the distance between the inside edges of the joists. Measure the length of the wall that you're placing.
Cut one 2- by 4-inch board for each 16 inches of wall length. Make each board equal to the distance between the inside edges of the joists.
Position the boards between the joists, even with the bottom edges of the joists. Toenail them into place with 10d nails and a hammer.
Move the wall into position. Push wooden shims in between the top plate of the stud wall and the boards you've placed. Snap off the excess wood of the shims.
Nail through the top plate, through the shims and into the boards with two 10d nails at each point where they intersect.