One of the best things you can do to help yourself at Stanford is to find the people who are doing work that interests you and go talk to them. They are experts in that field, and once you are connected to them, you’ll have a better chance of learning about related opportunities and understanding the broader landscape.
So when you know what you are interested in, how do you find the related faculty? A few suggestions:
ExploreCourses—drop some keywords into ExploreCourses and see who teaches those classes, and in what departments (including in the graduate/professional schools).
Faculty Profiles—department websites will have a People or Faculty link somewhere, that will usually have a little paragraph about each professor’s research and publications or a link to the professor's own site. The Stanford Humanities Center lets you browse their Experts Bureau. Engineering produced a faculty research guide in 2012. People in the School of Medicine, and possibly other schools, will be on the new Stanford Profiles website. The list of Research Centers at Stanford may help you find faculty who are not teaching or not attached to a department.
Stanford News—the Stanford Report and The Dish both cover research and professional activity on campus, as does the Stanford Alumni Magazine. Searching for topics that interest you can help you both identify faculty and give you good background information and questions to ask.
Ask around—at the end of each conversation you have, ask “is there anyone else I should be talking to?” Experts know other experts.