This can be done by bus and now also by train.
As you’ve seen from our previous posts, if public transport is your preferred method of getting around – then head out of the arrivals terminal and go to the bus stop across the road to wait for the 175 bus. This is a great regular bus and should take 30mins or so to get you into the centre. You can also buy tickets from the machine at the stop or on the bus itself. The buses run every 10 mins or so. You can check the timetable in English here: http://wyszukiwarka.ztm.waw.pl/bin/query.exe/en.
Read more about the transport into city centre on the Warsaw Airport information site: http://www.lotnisko-chopina.pl/en/passenger/access-and-car-parks/Public-transport
Warsaw Stadium (Warszawa Stadion) has its own train station so you could get a train from Warsaw Central station to the stadium station, or get a tram across the river (Central station and East/Stadium stations are on opposite sides of the Vistula river).
Warsaw Chopin Airport now has its own train station too where you can get trains into Warsaw East and Warsaw Central every 10-12 mins in the morning & afternoon rush hours. The journey will take 25mins to Warsaw Central and 30 mins to Warsaw Stadium. Read more about the train here: http://www.lotnisko-chopina.pl/en/airport/about-the-airport/pressroom/news/2012/6/train-service-to-chopin-airport-now-available.
The trains are being run by Koleje Mazowieckie – the trains from the Airport to Warsaw East are every 30mins/1hr, so the fastest way is to get on any train to Warsaw Central and change there for Warsaw Central or Warsaw Stadium. You can see the train timetable in English here http://www.mazowieckie.com.pl/en/.
The other good news is that the tube (metro) and buses (autobus) will be running longer & more frequently in Warsaw during the Euro 2012 and the night buses will also be running more frequently throughout the night.
And saving the best to last – Euro 2012 ticket holders will also enjoy free travel on the trains, tube and buses from the midnight before the match to the midday on the following day after the match. More information here: http://www.ztm.waw.pl/aktualnosci.php?i=726&c=100&l=2.
Read more about Poland on our Euro 2012 Poland guide page : http://www.inlovewithpoland.com/euro2012-poland.htm.