Your back is composed of several powerful muscles: The latissimus dorsi, which extends from your waist to your armpits and creates a pleasing "V" shape when well-developed; the trapezius, a rough diamond shape that's at its widest between your shoulders and extends up into your neck; and the erector spinae, responsible for extending your back, keeping you upright with good posture instead of slumped forward.
Pull-ups
Pull-ups are the ideal exercise for strengthening the latissimus dorsi. The teres major, sometimes known as "Lat's Little Helper," also works during pull-ups. In fact, every single muscle in your back, from the rhomboids in between your shoulder blades to your trapezius, is called into action when you perform pull-ups with a variety of grips. Consider purchasing a no-mount pull-up bar that braces on top of a doorway, no hardware or drilling required, and has both wide and narrow grips so that you can do wide, narrow and underhand grip pull-ups. Just hold the bar and pull your body up to it, then lower.
Rows
If you have a single mid-weight to heavy dumbbell at your disposal you can do wide or narrow rows, which focus on your traps and lats respectively. Prop your left knee and left hand on a bed or other flat, firm surface and hinge forward from the hips so that your upper body is horizontal. Keep your shoulders level as you grip the weight in your right hand and lower it directly below your shoulder, then pull it up and back. Keeping your elbow close to your side as you do this--a narrow row--focuses the effort on your latissimus dorsi. If you let your elbow flare out to the side, your traps are activated; in this case, pull the weight up, out and only slightly back.
Straight Leg Deadlifts
Straight leg deadlifts are the closest you can get to simulating a back hyperextension bench, another effective way of working the erector spinae, when working out at home. Grasp a dumbbell in each hand, palms facing back toward you, weights resting in front of your thighs. Hinge slowly forward from the waist, keeping the weights against your legs, slowly lowering them down to knee height. Keep your back straight as you do this, neither slouched forward nor arched, and look straight ahead. Squeeze your hips forward at the bottom of the motion to bring yourself back up to an upright position.
Back Extensions
Back extensions help strengthen the erector spinae, encouraging good posture as they combat the forward slump encouraged by sitting at a desk or working on a computer. To do back extensions, lay face down on a mat. Bring your shoulder blades in and down--think of sticking your chest out--and exhale as you lift your shoulders slightly off the mat. To make the exercise harder, extend your arms straight overhead, thus increasing the length of your upper body that you're expecting your erector spinae to lift.
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