You can take Caltrain to the Stanford Stadium Station for all home games. There are three games left in the regular season: November 7 vs. Oregon, November 21 vs. California, and November 28 vs. Notre Dame.
The Stanford Stadium Station is a platform only. No ticket machines, and you cannot buy tickets on the Caltrain itself. Also, this a Caltrain service, not something organized by Stanford University. Sometimes the school does not open the gates as early as they say they will, in which case the trains will let early arrivals off at the Palo Alto Station half a mile to the north.