What are the rules for inheriting a home in California? Does the person inheriting have to pay taxes on the home when it is sold?

The person inheriting it has to pay taxes on proceeds from the sale, yes. Since the house becomes theirs in an inheritance, it is like if they sold any home.

As an heir you do not owe any taxes when you inherit property - there is no inheritance tax in CA. But when you later sell the property you may owe capital gains taxes if the property appreciated in value during the time you owned it. Your cost basis for determining whether you have a capital gain is the fair market value of the property as of the date of death of the person you inheited it from. The executor of the estate is responsible for telling you what that amount is.