In order to finish your basement, you will need to frame corners, doors, and ceilings. These tips will help you with the job.
Build a 3-stud corner where the framing meets at the corners. When you start framing your walls, nail three studs together and place them at the end of the plates, then install your other studs on their 16-inch centers.
Fasten the first wall section in place, then build your second wall section. With the second section, install a single stud right at the end of the plates, where it will butt against the three studs on the other wall section. Fasten the corners together by nailing through the single stud into the three studs.
If you need to run any wires or cables through your corners, you can alter the design slightly by using 2x4-inch pieces sandwiched between the two studs, rather than a full stud. Using pieces will give you an opening through which you can run cable.
Your framed walls will likely need to accommodate doors. Make sure your finished door openings are large enough to easily move furniture in and out of the room. You should install at least a 32-inch wide door.
To allow for installation of the door as well as the casing, plus have room for shimming the door, you should frame the opening 2 inches wider than the door itself. For example, when using a 32-inch wide door frame the opening at 34-inches.
Frame extra space above the door, about 1.5-inches more than the height of the door. Since standard doors are 6-feet, 9-inches tall, your framed height should be 6-feet, 10.5-inches from where your finished floor will be. Use straight studs to frame the doors. Adding some extra side bracing will help stabilize the door.
If you are planning to install a drywall ceiling, you must provide structure to attach the drywall. The easiest way to do so is to run 2x4-inch boards perpendicular to the floor joists on 16-inch centers. Doing so provides a solid foundation to hold the drywall as well as lots of room for running wires or plumbing pipes above the ceiling.
The obvious downside is that you will be losing 2 inches of ceiling space. If you are going to install a suspended ceiling, you don't need to worry about framing the ceiling.