As of today no regular flyghts to Sumy.
From Kyiv: 4 daily trains
From Kharkiv: 5 daily trains
From Russia: by train Moscow-Sumy or by lot of trains with changing in Konotop (120 km from Sumy)
For timetables see site of the Ukrzaliznytsya [wiki=befc07801218b27021a0ddf7bd8722e8]http://www.uz.gov.ua[/wiki]
Regular comfortable minibuses (marshrutkas) from Kyiv, Kharkiv, Dnipropetrovsk. You can use it by 2 ways:
1) call to the bus-company for booking place in the mini-bus (+380542600089 to Elit-express, +380509339093 to Sun-auto)
2) go to the place of departing and ask driver about free places. In Kyiv it is close from central railway station (to the left after exiting from the main entrance). You should seek minibus (Mercedes or Volkswagen) with russian tablet "Сумы"
The best way will be rent a flat. Ask at the newspaper kiosk about newspaper with ads.
Zdybanka [http://www.zdybanka.com/]
Shafran [http://www.shafran.sumy.ua/]