Standing beneath the pull-up bar, reach up and grab the bar with a slightly wider than shoulder width grip, palms facing forward. Keep a slight bend in the elbows so they are not fully locked out. Allow your body to hang, bending at the knees and crossing your legs behind you at the ankles (if necessary for your feet not to touch the floor).
Pull your chin towards the bar until it touches the bar, then slowly return to the hanging position, stopping just shy of lockout. As you perform the movement focus on pulling with your elbows. This will help you use your back muscles to complete the movement. Try not to pull with your biceps as you complete the exercise.
The key with pull-ups is that the more you do them, the stronger and better you get. I suggest performing as many repetitions as possible, then resting for approximately one minute, and repeat for multiple sets.
The back is a very large muscle group. You can effectively hit different areas of the back simply by changing your grip.
My favorite grips are as follows:
Wide Grip Pull-Ups - Described above
Neutral Grip Pull-Ups - Palms are facing each other (Your pull-up bar may not have this option)
Medium Grip Pull-Ups - Shoulder width, overhand grip
Chin-Up - Underhand grip, closer than shoulder width