Tartu Airport: http://www.tartu-airport.ee/eng
Lennart Meri Tallinn Airport: http://www.tallinn-airport.ee/en
Hourly express Tallinn-Tartu. The express stops at the airport in Tallinn on the way to and from Tartu. Tickets can be bought from the driver providing there are free seats (10€ one way). The distance between Tallinn and Tartu is 186 km which equates to 2 h 25 min of travelling time by bus or train.
Comprehensive bus timetables: http://bussireisid.ee/en
There is also the option to use the train to travel from Tallinn to Tartu but the service is not as frequent as the bus: http://elron.ee/en.
The downtown of Tartu is conveniently small for getting around on foot. The conference venue is 2 km from the centre of the town which is about 20...30 min of walking time. Two public bus services, No 6, and 16 take you to the venue. Tickets can be bought from the driver for 1€.