The best way to get to bialystok is by taking a plane to Warsaw and from there either a bus or a train. The trip from Warsaw to Bialystok should take aprox. 2-3 hrs.
The city is not that big, and if you do want to explore it is best to walk. You may as well take the bus or a taxi.
Take a train from Warsaw or other big city in Poland.
You can also come here by bus.
Bialystok is not that big, so you can walk everywhere admiring its beauty.
Once you get tired you can take a bus or a taxi.