This is very sweet of you. You did not say how old you are; that will matter because the procedure is different for a minor versus an adult. The california courts have a great website that has all the forms you need to complete this process -- copy the link below, or google "California courts name change" and the california courts slef-help center will come up.
You can type in the information the forms, print them out and take them to the court. The back of the Petition for Change of Name has instructions for all the steps you need to complete. There is a court fee for the petition, but you probably qualify for a fee waiver. You will need to fill out the Application for Fee Waiver (also available at the california court's website) and take it with you to the court along with the other documents.
Make sure you carefully read all the instructions. You must serve your Dad if you are under 18 (actually, your mom will have to do the petiton if you are under 18), and there is also a requirement to publish the information in the newspaper. If you are under 18 and your Dad files an objection, there will be a hearing, and the court can deny your petition if it finds that it is not in your best interest to change your name. However, if your Dad does not object at least two days before the hearing, then the judge can enter the order without a hearing. Ask the clerk when you file how you will get the order if there is no hearing -- you may have to go back to the court to pick it up.
Best of luck to you!!