Useful information about Tartu can be found here: http://www.visitestonia.com/en/holiday-destinations/city-guides/tartu-tartu-university
Tartu has direct bus connection from Tallinn Airport (2 h) and Riga airport (3,5 h). Also, one daily international flight from Helsinki, Finland.
Additional information about transportation possibilities in Estonia (and to Tartu) can be found at http://www.visitestonia.com/en/travel-transportation/travel-around-estonia
Enjoy your stay ;)