Build where? SF is hemmed in by hills and ocean. Housing is mostly low rise, but dense and very much in the style of Tokyo given similar issues (earthquakes). Then you have a bunch of beautiful Victorians to tear down before you can build some dense high rise housing.
SF is quite dense already, not like the exclusive suburbs to the south.
In a normal place this is accomplished by increasing building height, increasing the building's footprint and reducing the unit size. No additional land needs to be used and higher density increases efficiency of services such as mass transit as well reducing environmental impact.
Unfortunately SF has some of the most restrictive zoning rules anywhere and, as described in the article, construction usually involves evicting tenants paying well below market rent. Given the highly litigious and politicized environment it is much more likely to get worse than better.
I mentioned Tokyo, which is as low rise as SF. You can build up on faults, but the construction costs (use more steel) are much higher, so it happens less often than geologically more stable locations (like NYC).
SF is quite dense already, not like the exclusive suburbs to the south.