You can build a thin interior wall the same way you build a regular wall, just with thinner boards so that the wall doesn't take up as much space. The only issue with this is that the boards aren't sturdy enough to truly hold up the heavy drywall panels, so you must use something else, such as lightweight wood panelling.
Locate the ceiling joists and floor joists where you want the wall placed. Use a stud finder to help you find them.
Measure the wall area and cut two 2-by-2 wood strips for the ceiling and floor plates.
Lay down one plate and measure in 1 1/2 inches from one end. Draw a line across the wood to mark the measurement. You will put the first wall stud between the end of the board and the mark. Measure from the end out along the length 16 inches. Make a mark, and then measure 1 1/2 inches from this mark to make a second mark. This is where you place the second stud. Repeat across the wood.
Place the second board next to the first and mark it the same way.
Lay one of the boards down on the floor where you located the floor joist. Drill four-inch screws through the board and into the joists. It is best to drill pilot holes first since the wood is only 1 1/2 inches thick. Attach the board to each joist.
Hang a plumb line from the ceiling to locate where the ceiling plate needs to be in order to line up with the floor plate. Place the ceiling plate 2-by-2 board up to the ceiling and attach it with 4-inch screws. Measure the distance between the ceiling and floor plates. Cut additional 2-by-2s to this height.
Insert the boards in between the plates. Drill 3-inch screws through the studs and into the plates to attach them.
Hang wood panelling to the studs with tacks. Tap the nails in with a hammer. Leave a small 1/16-inch gap between panels for expansion. Drywall is normally used on walls, but with a thin wall, the drywall is a bit heavy. Lightweight panelling is better.
Trim the panelling to fit the end of the wall. Use a power saw to rip the panelling after you measure the space. Repeat on the other side of the wall.
Cover the end of the wall once both sides are panelled. Measure the end and cut a thin piece to fit the edge. Tack it into place as you did the others.