Attach the base plate of the wall to the floor. You can do this with a powder actuated nail gun or with a hammer drill and concrete screws. Because basement ceilings are low, it's usually easier to attach the plates and then build the wall in place, rather than building the wall on the floor and standing it up.
Attach the top plate of the wall to the underside of the floor joists by screwing or nailing it into the joists. Be sure that the top plate is directly over the base plate by holding the string of a plumb bob against the underside of a joist and adjusting it until the point of the plumb bob is touching the edge of the base plate. Mark this point and align the edge of the top plate to it.
Measure the vertical distance between the bottom of the top plate and the top of the bottom plate. Cut a stud to this length using a circular saw. Place it between the plates, be sure that it is perfectly vertical using a four-foot level, then nail, or screw it into place.
Continue along the wall installing all of the studs in the manner described in Step 3. Leave exactly 16 inches between studs to accommodate insulation.