Property taxes are 1% from the state plus local ad ons from bonds + Mello roos which is another local thing. In SF they are about 1.14% of value every year and it can fluctuate based on city investments (bond yields) to be as much as 1.18% or as little as 1.12%. Property taxes can go up as much as 2% per year on the assessed value based on the 1978 Jarvis Gann initiative known as Prop 13, also called rent control for home owners.
They are due in 2 installments, late December 10 and April 10, after which there is a 10% penalty. The installments cover July 1 to December 31 (paid December 10) and January 1 to June 30 (paid April 10).
When you buy a new property you pay at the old rate until the county catches up with you and sends a supplemental tax bill to make up the difference from your date of purchase.