Białystok is a 2½ to 3-hour train ride from Warsaw on the PKP Intercity line — the most comfortable way to arrive. Trains run roughly hourly through the day from Warszawa Centralna, with a few direct international services continuing east towards Vilnius and Hrodna. Tickets are inexpensive by Western European standards; book online via the PKP Intercity app for the cheapest fares.
The bus is slightly cheaper and slightly slower — Flixbus and the older PKS lines run from Warsaw and from most regional towns. The city's bus station is right next to the railway station, about a kilometre west of the central market square.
Białystok–Krywlany airport handles only small charter flights; for international connections, fly into Warsaw Chopin and take the train.