Go to the DMV with a parent. A new permit will be printed out for you so you can continue to drive. The next time you have a lesson, your instructor will sign it.  There is no law in the California Vehicle Code that says your permit needs to be signed by a driving instructor.  Your permit is legally valid if you passed the permit exam and the DMV issued the permit.  The only page of your permit you are legally required to carry when you drive is the first page with your name, address and licensing information on it.  (…but it is best to keep the pages together as you will need the second page attached and signed when you go in for your DMV driving exam after you complete your training.)