Funding from the University such as the Mentored Research Award and the UC Dissertation-Year Fellowship are administered by the Graduate Division. For a complete list of the fellowships available, the criteria for the award and the application deadlines, please see the Graduate Division's Financial Aid web page.
Investigate these at least one year before you intend to use them since the application process for most of them is quite lengthy. In some cases, e.g., the National Science Foundation Fellowship, you must apply early in your career before you have too many graduate units to be eligible.
A full list is available from the Graduate Fellowships Office, as well as applications for some of the major awards such as NSF.
You can apply for some extramural fellowships through the IB Grants Office in 40 Giannini. With your mentor's approval, the department will help you submit proposals for NASA and NSF Fellowships. Students are encouraged to write grant proposals and to develop them in conjunction with faculty members. Numerous sources of support exist within the Department and its associated research units. Consult our Grants Administrative page and List of Funding Sources for details.