What You'll Need
A pull-up bar, which clearly comes as a surprise. And a love for variety, aka, the spice of life.
Why You Should Be Doing This Exercise
Life's problems can generally all be solved by doing more pull-ups. Okay, so we're prone to habitual line-stepping, but that doesn't mean the value of pull-ups should ever be understated. You will be a better athlete if you do pull-ups regularly (and if you tire of doing them one way, give Coach Demayo's article a read on pull-up variations... Variety is the spice of life!... Or something).
The progression here will take you from regular pull-ups to alternating grips, to chin-ups. Knowing this, let's get you in a pull-up position. So, hand width is entirely within your discretion. Keep em close to work the inner lat, and widen them out to hit the outer lat. The wider out, like twice your shoulder width, the more lat intense the exercise becomes.
Let's treat the middle of this like the middle of the exercise, and not the middle of a rep. Knowing that, after completing a set of pull-ups, your next set will have your right hand facing you (in a chin-up grip) and your left hand facing away from you (in a pull-up grip). After completing a set like that, now place your right hand in a pull-up grip, and your left hand in a chin-up grip. Okay, that's three in the bag. Now, for the finale, assume a chin-up grip with both hands. See, not so bad.
Not much to say here, but to remind you that a true rep, regardless of what grip your using, involves lowering yourself to an arms extended position before pulling yourself back up (trying to bring your upper chest to the bar while keeping your legs straight and together). Anything less would frankly be uncivilized.
Since we discussed what constitutes a true rep in the finish portion of this exam, we'd rather not repeat ourselves. We will gently remind you to breathe while doing these, as there's this odd tendency to hold one's breath, as if air will knock the bar down. Also, let's avoid the lower body swinging because it just doesn't look good for anyone involved, which would mainly be you.