Pull up is probably the best bodyweight back exercise out there. It will primarily target your lats while also working your biceps and shoulders. You will need a pull up bar but they can be bought cheaply on the internet or at any store that carries sporting goods. Using a grip that is a little wider than shoulder width, you want to grab the pull up bar with your palms facing forward. With your arms extended and holding the bar bring back your torso around 30 degrees and stick your chest out while exhaling. Pull up your body until your chin is above the bar by drawing the upper arms and the shoulders down and back.

The polling is done primarily with your back muscles rather than your biceps. pause for a moment and then return to the original position. During the motion your forms should not move as they only hold the bar if you don't have enough strength to perform this exercise as a spotter to hold your legs or start with a slightly easier Chin up first.