Measure the length of the space where you plan to erect the first wall. Cut a 2-by-4 to the same measurement for use as the top plate with your circular saw. Have an assistant hold the top plate against the floor joists along the basement ceiling. Use a power drill to make pilot holes through the top plate and into the joists above it. Use your screw gun to drive in drywall screws to fasten the plate in place.
Attach a plumb bob to the outside edge of the top plate at one end. Allow the bob to hang straight down so it touches the floor below. Mark the location on the floor using your marker. Move the bob to the other end of the top plate and perform the same steps. Use these marks as the location guide for the bottom plate.
Cut 2-by-4 inch lumber to the same measurement, and lay it in place on the basement floor. This will serve as the bottom plate. Use a power drill and wood cutting bit to make pilot holes through the plate. Use a masonry bit to make pilot holes into the floor directly beneath the plate. One hole every 16 inches or so will do.
Drive expanding anchor bolts through the plate and into the floor with a hammer. Thread the nuts onto your anchor bolts and tighten them all the way with your wrench.
Measure the gap between the top and bottom plates at both corners. Cut 2-by-4s to fit the gap and install them onto the plates. Drive 8-pound nails into the base and top of each stud so it's toe nailed in to the plates. Repeat the process and place one stud every 16 inches on center throughout the length of the wall.
Repeat the framing process along every basement wall. In the corners where two walls meet, allow one to abut against the corner, and cut the other 3 1/2 inches shorter so it fits flush against the first wall to create a tight fit. Build up the corner joint with two full length studs placed flush against the vertical stud closest to the concrete corner. Nail all the corner studs together so the two walls are anchored as one.
Install drywall sheets over the wooden framing.