From Europe, Asia and North America you can get to Sumy by air, transferring in Kiev (Boryspil International Airport or Kiev Zhuliany Airport) or Kharkiv. From those airports you can take a train, bus or mini-bus to Sumy.

Kiev Boryspil International Airport, service by all major airlines
Kiev Zhuliany Airport, service by discounter airlines including WizzAir, Vueling and FlyDubai
Kharkiv International Airport, service by more than ten airlines
How to get to Sumy from Kiev Boryspil Airport, Kiev or Kharkiv