Train
There are 3 or 4 daily suburban trains to/from Yaroslavl, an overnight fast train to/from Moscow’s Savyolov Station, no services to/from Ivanovo or Vladimir.
Bus
There are buses to/from Moscow (6 daily), Yaroslavl (8 daily), Ivanovo (8 daily), Vladimir via Suzdal and Vologda (daily).
Boat
If you are coming to Kostroma on summer, the best way to get there is by hydrofoil. Hydrofoils run twice a day.