Insurance cost will vary massively by area. You'll need to contact an insurance agency and get quotes for a landlord policy. You'll want good liability coverage. I could tell you what I'm paying in Tennessee, but it is unlikely to have any relation to what it would cost you in CA (I also live in CA, and my homeowners is way more expensive than my landlord policy for TN).
Generally, you are supposed to inform your lender of your intent to rent out the house. Check your mortgage paperwork.
