Many opportunities exist for undergraduate and graduate students to become involved in archaeological field work -- in fact, participation in field research is one of the requirements for the undergraduate major. Current research projects are underway in Çatalhöyük (Turkey), Chavín de Huántar (Peru), the Stanford Gym on campus, and Pueblo History Field Project, American Southwest.
For information on a specific faculty member's project, it is usually best to contact that person directly. You are also welcome to stop by the Archaeology Office and leaf through the Archaeological Fieldwork Opportunities bulletin, published by the American Institute of Archaeology (AIA).
Undergraduates should check out the office of Undergraduate Research Opportunities, located in Sweet Hall. URO offers funding for undergraduates who want to pursue independent research projects. They have firm application deadlines, so be sure to check their site early and often!