I do a lot of work with an LLC that renovates homes in the bay area, so I have a fair amount of experience with this. Generally, it's not too difficult to get permits for additions, but this can depend greatly on the specific home. Like Gregory said below, there is a limit to setbacks from all sides of the property, and there is a minimum amount of outdoor space in a given property that can not be covered by the home itself.
In addition, there are height limits, and restrictions regarding how close to your neighbor's home you can build. If you're adding space into existing interior square footage that is currently not living space (garage, attic, storage room, basement etc) there generally is no problem getting a quick permit. The more complex the addition, the more difficult your permit may be.
If you'd like any more information, let me know a little be more about what type of renovations you want to do, and what home you'd like to do them on, and I'll do a bit of digging to see what I can find.
Hope this helps!