The largest airport is located in the capital of Poland - Warsaw.
Once you arrive at the Warsaw Fryderyk Chopin Airport, you can take bus nr 175 to the central railway station (Warszawa Centralna) and then a train to Olsztyn.
If you choose to travel to Olsztyn by coach, it will take you about 3 hours. You can choose the airport in Gdańsk as an alternative. Once you arrive at the Gdańsk Lech Walesa Airport, you can take bus nr 210 to the central railway station (Gdańsk Główny) and then take a train to Olsztyn.
The journey takes about 3 hours. There is also a direct transfer from the airport to Olsztyn by coach.