The pullup can be performed with any of a variety of hand spacings, from wide to close, overhand grip (pronated, frequently called “pullups”), underhand grip (frequently called “chinups”).
Start from a dead hang, so that your shoulder blades are stretched, but do not go limp. It is important that you maintain tension by keeping “active shoulders.” This means actively pulling your shoulders into the socket and to maintain this throughout.
In a smooth motion, pull yourself upward in a manner commensurate with your hand spacing. If you have a wide hand spacing, your elbows will travel out to the sides of your shoulders. If you have a close hand spacing, your elbows will pass in front of your body. At all times, try to think of “pulling your elbows down” rather than pulling your body upward. This tends to help people develop that elusive “mind-muscle connection”, which tends to be very difficult for some people to develop for the posterior of their bodies, especially the lats.
Go as high as you can, at least to your neck and ideally to your chest, and then lower yourself under control. Again, think of allowing your elbows to go up, rather than thinking of your body as lowering.
Doesn’t matter, really. Use whatever you’re strongest at. The delineation between chinup and pullup is overemphasized in importance. Most newbs will be strongest with a grip that is parallel (i.e. hammer grip), with a hand spacing just closer than shoulder width.
Whatever you do, pick one and stick with it and add weight once you can hit 10/12ish reps in a set. Go hard on these, don’t be afraid to use a little kick on your last rep, and have fun.
Doesn’t matter. Don’t obsess over whether you should do “chinups” or “pullups” or “behind the necks” or “wide grip front” or “medium grip” blahblahblah
just pick a grip and get better at it in a progressive manner. No, chinups aren’t cheating. No, chinups aren’t all biceps (can you REALLY curl your entire bodyweight?) Do whichever hand space variation allows you to work hardest and get the most reps with.
Mainly it depends on your goals. I think it’s worthwhile for many of us to train as many grips/variations as possible, like thickbar pull-ups, rotating bar pull-ups, ring pull-ups, towel pull-ups, kipping pull-ups, L-sit pull-ups, prone/supine/neutral grip pull-ups, one arm pull-ups, wide, narrow, etc! I don’t believe there is any one “best way” to pull our bodies up from a hanging position given the variety of physical obstacles that could fit the bill. These range from tree climbing, to wall climbing, to rope climbing, to sport climbing, to anything climbable. I relate this to the variety of ways that an object can be picked up off of the ground. Sure it would be nice to always lift things up with a straight back, but that isn’t always practical, so it makes sense to train with a rounded back too. Ultimately it needs to meet your goals though. So if you just want big strong biceps, do chins, but if you want to compete in Ninja Warrior or scale the Eiffel Tower, better train them all. And if you never have any ambition of climbing a tree or using gymnastic rings there’s nothing wrong with that either.
Rippetoe seems to advocate the supine grip chin-ups as his de facto choice of grip.
Here are some possible variations that you could incorporate.
(NOTE: He is not getting full range of motion on these, you should be going down until arms are fully extended.)
Rack chins are an outstanding way to get stronger at pullups, and they also make for a fantastic way for a bodybuilder type to learn how to hit their lats more directly with the various pullup grips.
Always strive to use full bodyweight, but rack chins can certainly be used if you are unable to do regular chinups. The primary suggestion is to add 2-5 reps per set, because they are easier. i.e. instead of doing about 8 reps per set, try to get 10-12 per set if you do them rack-style. Be very wary of the angle of pull. Don’t allow this to turn into a swinging body row-up. Do these VERY VERY STRICTLY. There is no excuse for cheating on this exercise.
Jumping pull-ups and band assisted pull-ups are another alternative. And you can even incorporate slow negatives into them also, but continue to strive for that bodyweight pull-up. Go easy on the negatives at first, these can leave your arms tender and stiff for days to come.
Band assisted pull-ups: