Besides what  the Berkeley International Office (BIO) will tell you, here are some things to know and consider.

In the eyes of the University, a non-resident graduate student can only work a maximum of a 50% appointment on campus (resident students can work up to 75% appointments with out any other paper work). There really isn't any way to get around this 50% requirement unless you show "significant financial hardship". You can, however, work off campus by activating your CPT (Curricular Practical Training), but the job has to be relevant to your studies ...no Starbucks barristra work allowed. Simple paperwork, but it needs to be done a little in advance.
                

You can be an independent contractor/consultant. Don't bother letting the University know if you are going to do this. If someone would like to hire your for your knowledge of a subject area congratulations! There is a small blurb about contracting in the Grad Student Handbook. It basically says "some of our ESPM students get contracts/consults". When tax time comes you just need to fill out a 1099 form to claim the income.