B737 Undifferentiated or Other Model
Flight Crew Last 90 Days 130; Flight Crew Total 10000; Flight Crew Type 300
Human-Machine Interface; Confusion
Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Human Factors; Aircraft
Out of 8;000 for 6;000 (set in MCP) Captain was given approach clearance.  He tried to begin the descent with the autopilot coupled but was unable to get the FMA out of altitude hold.  Captain tried to enter Vertical Speed (V/S) and I think another mode.  The Captain disengaged the autopilot; began descent; and asked me to get the MCP/FMA into V/S.  I rolled the MCP to 5;700 and engaged V/S.  I believe it went to 1;300 because he was descending at that rate manually when V/S was engaged.  While this was happening the Captain lost sight of traffic we were following.  I was trying to look ahead left to find the traffic.  Captain asked me to arm the approach.  I armed the approach mode and queried about MCP altitude.  We set 0.  I tried again to find traffic and while looking we got a low altitude advisory from Tower.  Captain had leveled the plane and I reported level to Tower.  Captain joined the glidepath and recovered to safe operation.  The remainder of the approach and landing were uneventful.
B737 First Officer reports as pilot not flying; the inability of the Captain to initiate descent with the autopilot engaged during the FMS Bridge Visual to SFO. The MCP altitude is set to zero and the autopilot engaged to continue descent. Descent below charted altitude results in a low altitude alert from the Tower.