Extending a tourist visa (L) in Shanghai?

Hi, everyone! I've got a problem, and I am in desperate need of your help (sorry if something like this has been mentioned before).

I'm entering China on July 2 by tourist type, which will expire on July 31. I want to "renew" it for another 30 days. So the question is: when should I go to the Bureau to submit for the extension? And when then will be the expire date of the second one?
I just want to spend more time with my beloved, so I don't want to go too early. On the other hand, overstaying the limit is not an option.

Thanks for help!