Make a scale drawing of your basement on a piece of graph paper. Decide which walls you want to build and what you want to do with the spaces on paper. Things are easier to change and mistakes are less expensive to fix on paper than in the real world.
Determine the amount of lumber you will need for your framing project. For each wall, you will need a bottom plate to attach to the floor, a top plate to attach to the ceiling joist and a stud every 16 inches. You will also need to double up studs around doors and windows and install headers over doorways and window openings.
Assemble the walls by installing the top and bottom plates first then inserting the studs one at a time. Most walls are built flat then stood up as one piece, but the confined space of a basement makes building them in place easier than trying to stand them up.
Frame the exterior walls first if you are planning to insulate the basement. You may not need framed walls against the exterior walls, but it's recommended if you are trying to make your basement more heat-efficient.
Build the interior and dividing walls so that they butt up against the exterior walls. Remember to include studs at the corners of each wall to provide a bearing surface for the drywall.