The San Francisco Bay Area (click for map) has three large airports with scheduled passenger service. SFO and OAK are the likely choices for a trip to Napa, which is in the northern part of the area.
The Bay Area's third significant airport, San Jose International (SJC), is some 35 often-traffic-jammed miles further to the south, and would usually not be in the running for a trip to Napa unless you have additional business at Stanford/SLAC or in Silicon Valley.
Sacramento International Airport (SAC) is a mostly-domestic airport that may be more convenient for some. It is comparable to SFO or OAK in its distance from Napa, albeit in a different direction.
Most travelers would opt for either a rental car (to save money and reduce traffic and pollution, you may wish to compare notes with colleagues to see if sharing a car is feasible) or an "airporter" door-to-door shuttle.
The meeting venue is 62 miles from SFO, 54 miles from OAK, and 67 miles from SAC. The drive takes about an hour and a half off-peak; allow an extra hour (at least!) in commute traffic. Resources such as Google Maps or 511.org give realtime traffic estimates for various routings.
It is possible, but quite unwieldy (a 5-6 hour trip involving multiple forms of transportation), to get from these airports to Napa by public transit.