If you are coming via Tallinn Airport, you should take the direct bus to Tartu (operated by Lux Express).
The travel to Tartu takes approximately 2 hours 20 minutes, and the final bus stop is 100 m from Hotel Dorpat in Tartu centre.
It is advisable to buy the ticket in advance via internet (http://www.tpilet.ee/en/timetable/lennujaam/tartu) or at the ticket machine at the exit of the ground level floor (0-level, one floor below the baggage claim) of Tallinn Airport.
The local name for Tallinn airport is Tallinna lennujaam. This station name you have to type in Estonian…
Buying the ticket in advance is especially recommended if you are arriving on Sunday evening – many students are returning to Tartu after the weekend and there might be no more free seats available.
If you have bought your ticket via internet, you have to print the ticket out yourself. You can do this at your home or at Tallinn airport. The ticket machine at ground floor (0-level, one floor below the baggage claim) can print your ticket if you know the ticket number. Printing there is free of charge.
Also, it is possible to print your ticket at information desk, but this cost 1 EUR.
Some busses in the evening do not stop at the airport on their way from Tallinn to Tartu; to use these connections, you need to go to Tallinn central bus station. Use the city bus number 2 (direction Reisisadam, leave at 3rd station, Autobussijaam) or a taxi for transfer.