Measure the height and width of the wall. Sketch out the layout for the wall, assuming 16-inch spacing on the center line for the vertical studs. Purchase your top and bottom plates for the wall, plus the vertical supports. Since you're double-plating the wall, you'll actually be building two metal stud frame walls, one in front of the other. Plan your supplies accordingly.
Position the bottom and top plates for the first wall. Place the top plate in position first and attach it to the ceiling joists with wood screws attached through the mounting holes in the top plate. Drop a plumb line down from the top plate and mark the locations of the bottom plate onto the subfloor. Attach the bottom plate to the subfloor with wood screws placed through the mounting holes in the bottom plate.
Measure the distance between the top and bottom plates and cut your vertical framing studs to length with a circular saw and metal-cutting blade. Snap the vertical studs into position and attach with sheet metal screws through the mounting tabs of the plates and studs.
Position and install the second wall's plates 1 inch in front of the first wall. Make sure they don't touch, since a physical connection will aid in the transmission of sound waves through the walls. Install the vertical studs of the second wall after properly aligning and installing the plates as you did with the first wall.