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:
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.