I don't know anything about the Cameron school, but they have a website you can go to for information about their programs and what they involve. I do know some about testing in general, however. Any of the places you go would want basic background information about your child, his birth history (your pregnancy history), etc. to determine risk factors for hearing or developmental impairments. Even things like each parent speaking to the child in a different language (which lots of families do) will contribute to a speech delay, so those factors are all important to establish. Additionally, stuff like PG&E bills are used to establish that you do actually live in the county, because the county or the state are paying way more than what you will pay to the entity that is doing the testing--the equipment is pretty expensive and staff should be well-trained, and they (the school) gets subsidies so that parents do not have to pay the full burden, which is a good thing. Cameron School is part of the public school system, which may mean you pay nothing for their assessment, but that doesn't mean it doesn't cost the district anything to do it.
Another resource you can call is in West Berkeley, the Center for the Early Intervention of Deafness. They deal with all sorts of hearing impairments (which is often a reason for delayed speech), not just total deafness, and do great evaluations and help you with follow-up and advocacy. But they will require the same information, I'm sure--stuff like whether the baby was born early or exposed to certain antibiotics either before or after delivery is critical for them to know in order to help you out. Good luck, and (this is the hard part, I know well!) don't sweat the tests too much until you have the answers they give--remind yourself that what you see daily is the "very, very smart child who understands everything you are saying" that you wrote about. That means he is already compensating for any problems he may have developed, and that is a very good sign indeed. Just keep going forward remembering that the goal is your child's full development and the little roadblocks in the way won't seem so overwhelming!