I usually tell buyers it is 1.2% knowing that is higher than actual but that way your budget can't be suprised. It is actually 1.163% based on sale price which is the basis that is used by the assessor.
When you buy there is a day when you close escrow. At that point everything is prorated so if hte seller hasn't paid the taxes or even if they aren't due the seller pays up till that day and you take over from there.
Typically the City doesn't get everything together right away so you will end up paying the sellers tax rate for a while then you will get a new tax bill and you will also get a "supplemental" tax bill that is to collect the amount you owe at the new rate from the date of close of escrow.