AAA103 - 103rd WORKSHOP ON GENERAL ALGEBRA
The closest airports are in Tallinn (176 km) and Riga (254 km). However, there are much more buses between Tallinn and Tartu compared to Riga and Tartu (see the timetable).
Bus tickets can be bought online, but you can also buy them from a ticket machine at the airport or from a bus driver. A bus trip from Tallinn airport to Tartu lasts about 2 hours. The buses start from the Tallinn bus station, after 5 minutes they stop at the airport and then continue to Tartu. Normally you can get on the bus at the airport (if there are free seats or if you have bought your ticket in advance), you don't need to go to the Tallinn bus station. If you prefer a train trip, you must go from the airport to Ülemiste train station (1 km). Train tickets can be bought online, but can also be bought from the train conductor.
From Riga to Tartu, there are very few buses and no direct trains at all. You might consider an option of renting a car.