Teaching is a great way to share your passion about a subject, understand material better, and learn how to communicate clearly. There are a number of opportunities to gain teaching experience.
Biology requires 2-3 quarters of teaching assistantships, some Home Programs strongly recommend TAing for a quarter, and other Home Programs have no teaching requirements. See your Home Program's handbook for teaching requirements or recommendations. Regardless, most faculty and students believe that teaching is a valuable experience, and there are many opportunities to TA or teach in other settings.
Teaching Assistant (TA) positions
Graduate students often seek TA positions to gain teaching experience. Sometimes positions are advertised via Home Program email lists; many times, TA positions are filled without advertisement. The best way to find a TA position is to talk to the professor of the class in which you are interested in TAing.
Educational outreach programs for primary school students
Another way to gain teaching experience is through educational outreach programs. Stanford groups sponsor science outreach programs for elementary, middle, and high school students. See Diversity Outreach and Engagement for a compilation of outreach opportunities.
Mentoring younger graduate students or undergrads
Often, graduate students mentor younger graduate students or summer intern students. Talk to your advisor if you are interested in mentoring a summer research student through a program such as the Stanford Summer Research Program, Stanford Institutes of Medicine Summer Research Program, or one of the many summer internships listed on the Office of Science Outreach site.
Older graduate students also mentor first-year Biosciences students through the SBSA mentor program (information sent out each year on the SBSA listserv) or through the BioAIMS/SBSA fellowship mentoring program, organized for 2013 by Natalie Chavez (email).
For resources on how to be a good mentor, see Advising and Mentoring section—How to be a Good Mentor.