The first thing to consider is whether your basement ceiling is finished or unfinished. If it is finished, avoid drilling into it and use an alternative, such as a pull-up bar that mounts in the doorway, or a multi-function workout station. If the ceiling is unfinished, you can easily hang a pull-up bar from the rafters.
The most important decision you'll make here is how to hang the bar. You can mount your bar on the joists (the horizontal supports), on the wall, between two corners, above a door (using the top of the frame as support) or on the ceiling.
According to the home-improvement site HandyOwner.com, joist mounts and corner mounts are good for out-of-the-way locations; wall mounts are adjustable and strong (they attach to two frames that screw into wall studs) and door mounts can bear a weight of up to 1,200 lb.
The spot where you mount the bar must be able to support twice your weight. According to HandyOwner.com, the best places are a concrete wall, wall stud or ceiling joist. Choose a location at least 3 feet from the closest wall.
Materials and Tips
Tighten the bar with strong hardware. If you're supporting up to 350 lb., HandyOwner recommends 4 3/8-inch wood or masonry bolts. Drill pilot holes before installing the bolts to avoid cracking the wall studs or ceiling joist.