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.
Are you asking because you are buying a new home and wonder what to expect? On a new home purchase it is 1.163% of the purchase price. When you close escrow you will probably be required to reimburse the seller for property taxes depending on what month in which you close. And you will get a supplemental tax bill in the mail in the following 12 months or as soon as the city catches up with the sale. So in December, your bill probably will not reflect your new taxes, but it will reflect what the previous owner was paying and a supplemental bill will be on the way---you can count on that!
Here is a link that will explain what to expect :http://www.sfgov.org/site/treasurer_page.asp?id=8098. I hope this helps out! You can call me if you have any questions. Good luck!
Zephyr Real Estate-SOMA