The flexed arm hang is a good calisthenics exercise to start with, when pull-ups are still a bit to heavy for you.
Grasp a tree branch or the top of a high bar with your palms facing toward or away from you. Jump up and hang for as long as possible with your arms bent to a 90-degree angle (or fully flexed). Make sure that both feet are off the ground. Breathe normally as you hang and feel the muscles in your arms and upper-back contract. Rest for one or two minutes and then repeat.