Hmm there's really not much to acing pull-ups.
I used to hit only 6-7 during my Upper Sec days, but once I
reached JC and joined canoeing my pull-ups hit 22-25. And yes with
proper form...
1 very big misconception is that most people would do a close
grip pull-up (at shoulder width or more often than so less than
shoulder grip), this uses more of the triceps to do the pullup. And
most of the time most people have weak triceps- get my gist :)
First things first to use your lats, make sure you WIDEN your
grip. Initially it will be tough and you wont see much improvement,
your pullup count might also initially drop (some of my friends
experienced that) but it will gradually pick up and over time you
WILL see improvement if you continually train. Aim to do it daily
and 10 pull-ups per set (start with 2-3 sets per day and move to 10
sets). Do them within a limited time frame if possible (ie dont
space them out throughout the day).
TBH gym-machines dont really help much in improving your
pull-ups. They do help to strengthen your lats and biceps (to a
smaller extent) but they wont help to improve your pull-ups as much
as there's more to pull-ups than just pure lats/biceps/triceps.
Even abs (your core muscles) are utilised to some extent. So the
best to train for pull-ups is doing the method I outlined above.
Once you're confident of hitting the above-mentioned ranges, you
can hit the gym and do weighted pull-ups (placing a dumbell between
your legs).
It is only then should you start to focus on furthering your lat
muscles strength, and even then I dont recommend gym machines. Do
barbell pulls (aka bench-pull), upright barbell rows, one arm
dumbell rows etc etc.
Just my two cents worth- hope they helped :)