Becoming the legal guardian for Granddaughter in California?

Has anyone experience with the guardianship process in California. We've been supporting my sister and her baby since she was born, they've been living with us and the dad is out of the picture. Anyway my sister wants my mum to become the legal guardian for her baby, because she will be moving back to Europe in about 2 weeks. However, how long does the process take, and has my sister to stay here in the states until we have the guardianship? I also read about a private agreement, could we do that until we have the guardianship?