There exist several possibilities to reach Warsaw.
The easiest and most convinient way is to choose Chopin Airport in Warsaw. The airport is situated within 10km of Warsaw center and is connected with it by cheap, direct city bus 175.
Probably the cheapest airline operating on the Chopin Airport is Wizzair. Polish airlines LOT is the biggest operator here. Try to find some cheap flights on it´s website as well. Other scheduled airlines are listed here.
Another advisable way is to land on Cracow Balice airport. There is convinient rail connection to Cracow main train station (Kraków Główny), where you can take train to Warsaw. The train costs from 40 to 120PLN depending on operator. The route takes 2,5 to 3 hours.
Other Polish airports are less convinient to reach Warsaw.
Warsaw can be easily reached from Vienna, Berlin, Amsterdam, Kiev, Dusseldorf with overnight trains.