Lux Express buses depart hourly between 07:05 and 20:05 from Tallinn Airport ("Tallinna lennujaam") straight to Tartu. The bus stop is located on floor 0, i.e. by the car park that is located at the front of the airport, next to the so-called lower entrance.
Tickets can be bought online at http://www.tpilet.ee/en, from the self-service terminal in the airport or from the driver in case there are vacant seats. You can print out your tickets at home or use the self-service terminal at the airport.
It will take you 2 hours and 20 minutes to reach Tartu. Buses with free Wi-Fi are comfortable and offer some snacks and drinks for sale.
Other bus companies mostly do not stop in Tallinn Airport, so if you need to travel after 20:05, you should begin your journey from Tallinn Central Bus Station, which is easily reachable by taxi. Please find a suitable bus and buy tickets in advance at http://www.tpilet.ee/en.
New and comfortable trains from Ülemiste Station in Tallinn to Tartu depart eight times a day. Ülemiste train station is situated just one kilometre from the airport and is easily reachable on foot or by taxi.
It takes 2 hours to get to Tartu by express train. All the trains have free Wi-Fi access. Check the timetables and buy tickets at www.elron.ee/en. Tickets can also be purchased on the train.
Tartu Airport is located in Ülenurme, about 9 km from Tartu. It is possible to reach the airport using the taxi or AirportShuttle. AirportShuttle leaves Tartu Airport for the city about 15 minutes after the plane has arrived, but will wait for anyone who needs transport to the city. For a fee of 5 € the AirportShuttle will drop you off at any location in the City of Tartu. Tickets can be purchased from the driver, either in cash or with a debit/credit card.
One regular airline connects Tartu with the rest of the world via Helsinki. Finnair flies one time a day between Tartu and Helsinki, the flight lasts only 40 minutes.
You can also reach Tartu easily from Riga Airport (245 km from Tartu). Bus companies Lux Express and Ecolines operate the route Riga Airport-Tartu, timetables and fares can be found from here and here. No train connection is available.
Both in Tallinn and Tartu, all taxis have their individual prices marked clearly on the rear passenger-side window in English. To obtain a receipt for the ride, you must ask the driver at the end of the journey. Receipt is known as "cheque" in Estonia.
Taxis are available at the airports, bus or railway stations and other central locations, such as beside the Town Hall Square in Tartu and Tallinn. It is also very easy to order a taxi through Taxify app. The hiring charge is usually around €3-€4. Longer city trips are unlikely to amount to more than €5-€7. The rates charged will, to some extent, depend on the size and age of the car.
In Tartu the Central Bus Station, interesting sites, restaurants and hotels are so close to each other that it’s only a short walk from point a to b.