Build near mass transit and in walkable neighborhoods and restrict the number of parking spaces. Make streets safer to walk and bike. Adding more housing units doesn't need to mean a linear increase in cars as well.
That works if you have the land to do that. The Virginia side of the DC area has lots of high rise apartments and skyscrapers built around the metro station and it definitely works to keep cars off the road but I don't know of the same thing can be done in the bay.
> I don't know of the same thing can be done in the bay.
Walk by any of the BART stations in the East Bay (even Downtown Oakland), and you'll see vacant fields and mostly empty parking lots. The area near MacArthur BART could be densified to a crazy degree without displacing a soul.