Learning to be a grad student

I'm sure I've said it before. I've certainly thought it before. Either way, it bears repeating. Student/advisor relationships are hard.
I had a meeting with my advisor today to talk about work, and also about both of our recent travels, and while it went really well in many ways, and she was great and supportive and very helpful, I still found it really difficult to talk sense. I guess I'm still in the early stage of this setup, where I'm still trying to make a good impression, and I really am trying desperately to convince her that I am a student that she could want to work with. And so I feel like everything I say is over-eager and self-promoting, but at the same time lacking the substance that comes with experience and reading. I have so much to read before I can do good work. I have often thought about the process of becoming an academic as a sort of apprenticeship, where we learn from great scholars by watching them work, and working alongside them, and absorbing some stuff by osmosis, and other stuff through direct tutoring. But really, it isn't much like that at all. Our professors give us reading that they have done already, and have to re-read much of it themselves in order to lead discussion, despite the fact that it may not fit particularly well with their own work. They then have to read our efforts, and spend time helping us improve our work, and somewhere in amongst all that, they have to fit in their own work, much of which we as students are unlikely to hear about, because we are too busy with our own concerns. I feel a bit like I have to be more together and smart and productive, just to give my advisor a motivation to work with me in the first place.
I do have a super advisor, though. And that is worth a whole lot.