Tallinn airport has direct flights to a number of European cities and many flights a day to airports in Helsinki and Stockholm where it is easy to find connector flights to other destinations. Connector flight from Helsinki to Tartu is available once a day.
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.
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.