Residency

If you are not a California resident, you must apply to be one before the beginning of your second year to avoid paying nonresident tuition. To become a resident, you must show that you have been in the state for at least a year and that you plan on making California your permanent home.

You should do the following things upon arriving in Berkeley:

Keep all documents confirming your arrival in California: plane tickets, receipts
Apply for a CA license as soon as you can and register your vehicle
Register to vote in California, and vote in the next election (save your voting stub)
Change your permanent address to California with the post office, your bank, credit card companies, etc
If you open a California bank account, save your opening statement and the closing statement of your old account. Otherwise save the first statement that shows your new California address.

In June you will need to submit these documents to the registrar's office (along with tax forms and documents confirming your employment with the department). Failing to qualify for residency can create quite a mess, so take care of this.