| There is no honors "program" at Cal, unless you want to count the Regents/Chancellor's scholarship thing. As cnat says, it's by department -- meaning through whoever offers your major -- and related almost entirely to your GPA in courses in your major (with, of course, a minimum overall GPA requirement).
In the English department, for example, you need a 3.51 Berkeley GPA and a 3.651 major GPA (in classes taken at Berkeley) in order to apply for the Honors Seminar series, which is a 2 semester seminar class culminating in a long (40+ page) thesis. After all of this, you get to graduate with honors. | 
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