Measure the length of the wall you want to frame. This will give you the lengths of the top and bottom plates, which will be made of 2-by-4 inch lumber. The bottom plate should be made from pressure-treated lumber. Cut two 2-by-4 planks to this length.
Place the 2-by-4 planks on the floor so that they are parallel with each other and lying on their edges. Set a scrap of 2-by-4 between the two planks so that its outside edge is flush with their ends, then mark both planks using the inside edge of the scrap of 2-by-4 as your guide -- repeat the process for the opposite ends of the 2-by-4 planks. This will indicate where the two outermost studs will be.
Make a mark every 16 inches from the lines you made on both 2-by-4 planks. These marks will indicate where each stud will go.
Mark the floor with a chalk line where you want to install the wall -- if framing a cement-block basement wall, place the frame about a half inch from the wall. Use a laser level or plumb bob to mark the ceiling for the bottom plate.
Use a stud finder to locate the ceiling joists, which is where you will secure the top plate for the frame. Install the top plate by driving 3 1/2-inch nails through the plate into each joist. You will need a helper for this part of the installation.
Align the bottom plate on the floor, and drill holes through the bottom plate and the floor with a concrete bit. Then secure the bottom plate with concrete screws every 12 inches.
Measure and cut the vertical studs for the frame, using a circular saw or miter saw. If you are finishing a basement with a concrete floor, measure each stud individually to account for any unevenness in the floor.
Slide each stud into place, and check with a spirit level to ensure that each stud is at a 90-degree angle. Secure each stud by toe-nailing three framing nails on each end -- do two nails on one side of the stud and one on the other. Toe-nailing means driving nails at a slight angle. Repeat until you have installed every stud.