How to differentiate between the root cause and the branch?

Put simply, years of clinical experience is the only way to really improve with this. Because of the dynamic nature of Chinese Medicine you can fit many things into many different categories, but generally only a single or a couple treatment options will lead to clinical efficacy. I would suggest as you are going through school (and afterwards) that you find practitioners outside of the school to observe (and if possible assist) with. This will give you much more real world clinical experience even without applying the techniques yourself (which is actually the easiest part).