Pivot (formerly COS) is a for-fee database of funding opportunities and profiles of researchers. Berkeley subscribes through the Sponsored Projects Office and the database has been pre-populated for faculty and some graduate students.
You can use Pivot from any campus-based computer for basic searches without setting up an account. But if you set up an account, you will be able to log in from any location, and you will have access to the tools for managing searches and opportunities including the ability to set "alerts" -- where you are automatically notified of new opportunities that meet your search criteria.An account will also allow you to create, claim, or update a profile.
If you want to focus on funding sources for graduate students, in particular for the dissertation or thesis, go to the advanced search, scroll to the bottom and check the boxes next to Funding Type and Requirements.
Once you have a search you like, if you've created an account (free to you!) you can save the search and even receive a weekly email everytime a new funding source matches your search.