The easiest way to travel from Tallinn to Tartu is by bus. Buses between Tallinn and Tartu run every hour, sometimes even more often. The distance between Tallinn and Tartu is 186 km and travel time by bus is approximately 2.5 hours. Buses are usually comfortable and many offer WiFI connection making it possible to work while travelling. In Tallinn the buses stop at the airport and in Tartu the bus station is right in the city center requiring no additional transportation to the conference venue. Bus time table is available here where it is also possible to purchace tickets online.
There is also a train connection between Tallinn and Tartu. Express trains run 5 times a day and the travel time is just over 2 hours. WiFi connection is available in all trains. Train timetable and ticket information can be seen here.
From Helsinki there is a daily direct flight to Tartu operated by Finnair. The Tartu Airport (http://www.tartu-airport.ee/eng/) is situated in Ülenurme. The Airport Shuttle bus takes you to to the center for 5 euros, the ride takes about 20 minutes.
It is possible to travel to Tartu from Riga by bus but the travel time is longer than travelling from Tallinn - approximately 3.5 to 4.5 hours depending on the bus company - and buses do not run as often. For additional information see https://ecolines.net/en/ or http://www.luxexpress.eu/en.