Immediate caveat: I am garbage at pull-ups. I've mentioned that before, so when I say that I doubled my reps today, my pull-up performance has improved from "bad" to "slightly less bad." That said, I did genuinely make a big improvement with one simple form tip, which I am happy to pass along to you. 

The tip is called "breaking the bar," or "bending the bar." Here's the video that introduced me to the concept, which still could be a little more clear. In short, when you grip the bar, imagine that you're trying to snap it in half. This naturally adds external rotation, keeping the elbows in and transferring more of the workload to your back rather than your arms. It's a simple tip, but it absolutely works. The last time I attempted pull-ups, I did two sets of three (like I said, bad). Today, I did three sets of four, doubling my output. I still have a long way to go, but seeing actual improvement in one of my weakest areas is pretty encouraging. I used to dread pull-ups. Dare I say it, I'm actually excited to do more to see if I can keep improving.