There is no train station linking either Venice San Marco or Venice/Treviso airports to the city of Venice. From Venice San Marco airport you can take a bus (water bus) to the city or you can take a regular bus. The water bus is much quicker but costs around €10. The regular bus is slower but only costs a few euro.
From Venice Treviso airport you must take one of the buses waiting outside the airport (about €10) which take you direct to the Venice city bus station.