I was recently researching profiles on LinkedIN, (yes, I do stalk people) and I happened to come across someone who has been in the education industry forever. She graduated from Yale with 3 Master's degrees! With a degree in Philosophy, Arts and Ecology, I was heavily impressed. I was so inspired by her commitment, it gave me that jolt to keep going in my own education.
What could I say to this distinguished person?
Thank you. I sent her a message on LinkedIN and told her who I was, why I was looking at her profile, that I was impressed, and then I thanked her for her efforts and contributions. I did not ask her for a single thing, but reached out to express gratitude for the work she has accomplished thus far. This is true networking.
Taking the time to show that you are interested in someone else and their work is all it really takes. Don't worry about what you will get out of the connection, just make sure they know you are a fan.