There is a special train "Vilnius - Airport" running regularly from Vilnius railway station.
The ticket costs EUR 0.70. It can be purchased online, in the train and at the railway station.
Next to the airport passenger terminal, there is a railway stop, stairs and an elevator for passengers as well as lighting and passenger safety surveillance camera. There is a footway leading from the railway stop to the airport terminal for passengers; the footway has an installed gallery (it is illuminated during the dark time of the day).
Timetable and tickets: www.traukiniobilietas.lt