Make a mark on the beam where the new wall will end with a pencil. Measure the length of the wall with a tape measure.
Cut two 2-by-4 pieces of lumber to the length of the wall for the sole plate and top plate. Mark the positions of the studs on the plates every 16 inches.
Hang a plumb bob from the beam at a spot near the adjoining wall. Mark the spot and repeat for the mark on the beam for the end of the new wall. Use a chalk line tool to snap a chalk line between these two marks. Fasten the sole plate to the floor using a hammer and 10d nails, ensuring that it aligns with the marks.
Take the top plate and position on the beam it so it runs the length of the wall. Nail it loosely to the beam and check that it aligns with the sole plate. Fasten it securely to the beam with 16d nails spaced about 16 inches apart.
Measure between the marks at the first stud marks on the top and sole plates near the adjoining wall.
Cut a 2-by-4 to this length with a circular saw. Toenail it into place with two 16d nails on each side at the top and bottom. Measure the rest of the wall studs and fasten them in place in the same way.
Cut a 2-by-4 blocking piece to length and nail it in place 4 feet above the floor in the first stud wall cavity. Repeat for the remaining stud cavities.