First thing is to make sure that the stud product you use it rated(approved) for the area you live in. Second is to make sure that the studs are approved for the type of contact it will make(dirt, concrete,wood). Keep them on center as much as possible.
Measure the height of each wall so you can build frame. Buy the lumber to match plan and cut to correct sizes. Nail studs into footer with 10d sinker nails; use 2 per board. First attach end studs to header, then the middle studs. Be sure you have a square.
The studs on your basement walls are 4x6 vertical boards that are attached to the horizontal bottom plate and the horizontal top plate. Measure the space you need, cut your boards to the correct size and attach beginning with the top and bottom boards and then the studs. Ask at your local home improvement store for more detailed help.