The BART stations on Market Street were done as cut-and-cover jobs, obviously, since they extended nearly to the surface.
Between the stations, the tunnels were constructed by boring tubes, some of which were under pressure to keep out the water.
This article by San Francisco MTA has a good aerial view of Market Street showing the Montgomery Street station under construction, and how the MUNI streetcar tracks were re-routed along the sides of the excavation. Note that between stations MUNI was still running in the center of the street.