Caleb Pike of DSLR Video Shooter posted a video in which he shares some info on 5 skills that will make you a much better filmmaker - useful stuff especially if your task is to support a director. Caleb starts with tips on staging gear, because in his opinion it is one of the most important steps in production, besides you will be able to work more efficiently (things will be easier to find). In this case he focuses mainly on lights. Another huge topic is how you should behave on the set and why you should try to be subtle and quiet. You should also be asking questions if you want to learn something and achieve better results - you need to know what you're doing and why you're doing it. Additionally don't forget to be observant and try to study your boss to meet his/hers needs before asked.
"This post might just sound like a list of ways to suck up to your boss or director, but trust me when I say these skills go far beyond that. Today you could find yourself doing these things as an assistant, but one day you might find yourself on set as a director. Then you will need to know how to have your crew stage gear. You will have mastered the art of being a subtle director. You will know how to ask questions and discover new methods for doing things. You will be a master of observation and nothing will get past you. And finally, you will be able to study and serve your boss well and that boss won’t be a director, it’ll be the story."