>>2993985What I recently did for studying cinematography (you can do this to study photography too) was create a transparent framing guide with all of the lines I think are important and put it over frames from films to see where the elements of the composition are in relation to the lines. I normally take notes on patterns I notice, like how the edge of a person's face will often look better touching a third or golden ratio vertical line than if the line ran up the middle of the head.
This may be an overly-thorough method (I cropped all the terms for each line out of the pic related example) but I'm learning a lot fairly quickly. In my experience, it helps to have these compositional ideas in the back of your head while shooting.