In recent work with individuals who are renting in SF I would say that it depends on how much time you are planning on dedicating to full time rental searching. Both of my recent rental clients have found an apartment within 1-2 days while doing full day rental tours. The key is to be prepared with all necessary documents for applications (credit scores, recommendation from past landlords, proof of job, check.) Then when you visit a rental you like put in your application ASAP and express your interest. Good rentals go quickly but of you are vigilant you can get one. Best of luck!
I would suggest, if available, booking a temporary location somewhere between 1-3 weeks. This will give you time not only to find a place but to factor in the schedule of moving companies and the like. If you don't need movers then 1-2 weeks should be more than enough time to find a place and sign a lease. As Will wisely advised, be prepared and do move quickly once you find a place that meets your requirements.