What might you do in a typical first session with a student?

I like to get a feel for what the student needs help with, and what kind of learner he/she is (e.g. verbal, visual, etc.). I ask a lot of questions, and work from there to make sure that my style fits.

How can you help a student become an independent learner?

That's ultimately the goal, to give a student the right tools and structure to figure out how the language works.