I've always found a Socratic approach to work best - that is, letting someone reach an answer by simply guiding them through what they already know (versus telling them information). Even though this process can be time-consuming and even frustrating, the end result is always the same: people are amazed that they knew more than they thought they did, and they feel accomplished by having reached a result by using their own brain.

After personal introductions, I would definitely want to know a few things: first, what the student believes their strengths are, and what they believe they need help with. Second, what goal(s) they would like to achieve throughout the sessions. Third, how they typically approach studying in general. And finally, I would like to know if they've had a tutor in the past, and if so, what that tutor did that they found helpful/unhelpful.

I think the key to independent learning is showing a student that they do have, or can have, the information they need to reach an answer. Confidence is important. Positive reinforcement is also very effective, as well as asking questions of the student geared towards highlighting connections between what they do know and what they need to figure out.

Establishing goals early on, and as time progresses, reminding a student of how far they've come even in one lesson. I've also found that for me, making little checkpoints in just my daily work is crucial: for instance, grouping tasks so that the number doesn't seem so intimidating.