Although much of the student's time is filled with producing science, there are many opportunities at Harvard to take your interests in science and share them with broader audiences. Below are some of the science outreach activities that happen on campus and in the Boston Area. They are often looking for graduate students to give talks, or help with planning logistics.

The Arnold Arboretum of Harvard University:
The Arboretum's adult education offerings include classes in horticulture, botany, and landscape-related fields, focusing on programs that leverage the Arboretum's rich collections and expert staff. The Arboretum also offers numerous informal education opportunities—including tours, family activities, and exhibitions.

They are often looking for volunteers to interact with visitors and lead innovative Tree Mobs. They also have paid positions for FWSP-eligible students in their Visitor Center. For information on Tree Mobs contact Pam Thompson at 617-384-5277. To learn about volunteering with visitors or working in the Visitor Center, contact Julie Warsowe at 617-384-5253.

Café Sci:
Café Sci encourages open, easy-to-understand conversation about interesting topics in science. No lectures. No PowerPoint. No technical jargon. http://www.sciencecafes.org/find/02138

Science in the News:
Science in the News (SITN) is a program based at the Harvard Medical School that takes recent science topics that have been in the news and explains them to the general public. SITN produces a lecture series in the Fall as well as electronic newsletters. Several OEB grad students have been involved with this in the past. 
https://sitn.hms.harvard.edu/

NerdNite:
Nerd Nite is an informal gathering at which nerds get together for nerdery of all sorts (well, mostly presentations and drinking). 
http://nerdnite.com/

Harvard Museum of Natural History:
The HMNH is often looking for students to help teach short courses on broad topics related to natural history. 
Email: volunteers@oeb.harvard.edu
http://www.hmnh.harvard.edu