Just sit down and think not just about what a person said, but why they are saying it.

If my dad says, "Son, never date girls who are hippies", that probably means that he himself was burned from an experience like that. While reading it plain would have given me a catch-all theory that is not necessarily true, reading into the reasons told me two extra factoids: my dad doesn't want me to get hurt, and he has dated a hippie girl and that ended badly.

Someone told me once: "You're good at putting the puzzle together, but only when you have all the pieces."

I can't really give specific examples, but it really is a daily thing, where I remind myself to follow things to their logical conclusions, in order to know how to proceed with a task/project/question/etc..