The one component that you must have in a basement before you can install a shower in the space is plumbing. While most basements have some sort of plumbing running through them, not all basements have both hot and cold running water, which is a necessity for building a shower. If you have a washer in the basement, hot and cold running water should be available and you can tap off these lines for your shower.
The second main component that a basement shower requires is good drainage. If there is already a drain in the floor, consider building your shower over it. If not, you'll have to trench through the concrete floor and tie into an existing drain. Another option is to have the water drain into a sump pump.
Once you have water and drain available, you can build the shower. The shower should have have a base that slopes slightly toward the drain and curbs on all sides to contain water. Shower bases can be prefabricated from plastic or resin, or poured concrete.
After the shower base and shower walls have been put into place, you can use a number of different materials to cover the walls and floor. Ceramic or porcelain tile are attractive, while fiberglass shower enclosures offer a quick, inexpensive option.