You can choose out of few options to buy a ticket:
You can buy ticket from the bus driver (regular price: 1 euro, for students: 0,5 euro). The ticket will be valid until the end of the trip with bus. If you want change the bus, you need to buy another ticket.
P.S.Remember to mark ticket in the bus.
 
Other option is to buy „Vilnius Ticket“ (Vilniečio kortelė). Buy a card and e-tickets in a kiosk. For example: you can buy 30 minutes ticket, it will cost to you 0,65 euro. 1 hour – 0,90 euro. 1 day – 5 euros. 3 days – 8 euros.
When you activate your e-ticket in the bus, all this time you can use every bus or trolleybus in Vilnius.