To begin the chin-up, start with a supinated (underhand) grip, shoulder width apart. Picture your hands as hooks, and initiate the movement with your back, or more specifically, your lats. Before you begin the movement, take a deep breath in, bracing your abs.
As you begin to pull up, keep your elbows close to your body, and resist the urge to tuck your knees to your chest. Instead, keep your legs tucked BEHIND your body during the movement.
As you reach the top position, bring your chin over the bar, and touch the bar to the top of your chest. As you come back down, lower yourself in a controlled manner without dropping. This will overload the eccentric portion of the movement, while protecting you from injury. Once you finish the rep, take another deep breath, bracing the abs. Reset and begin another rep.