First option is to fly to Tartu. Tartu Airport has flight connection to Helsinki. The airport is about 10km from Tartu city center and express bus to and from airport is for free. More information in here.
Second option it to fly to Tallinn and take a bus from Tallinn Airport to Tartu Coach Station. Buses from Tallinn Airport are leaving to Tartu every half an hour. Here you can find the most suitable bus for you.