There are train routes which take you from Tehran and other nearby cities such as Arak, Yazd and Isfahan.
By train
Qom train station
+98/(0)251/6617141
By plane
By plane
The nearest and most easily accessible international airport is Tehran's Imam Khomeini International Airport IATA: IKA, ICAO: OIIE, which is due to replace the older Mehrabad International Airport IATA: THR, ICAO: OIII.
By car
By car
Driving from Tehran might be a reasonable option, however, if you're worried about driving in Iran you can reserve a private bus to take you to Qom. After all, it is much safer to travel by private buses.