This depends on the program you select. Certain plans require equipment, while others are completely equipment-free. You can always opt for the Home Athlete program, which delivers maximum results using only your body weight.
Some programs require equipment to do pull-ups on, like a pull-up bar or a pair of rings. Additionally, you will need parallel bars and/or a dip station, or a similar setup. Use resistance bands if you want to make some exercises harder, or add additional weights with a weight belt.