I checked the airport website, there seems to be a train but it's not very clear to me. Specially not knowing the names of the stations.
How can one get from Warsaw Modlin airport to Warsaw?
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You can use a special "Modlin Bus" - http://www.modlinbus.com/ which has a bus stop in front of the airport terminal and goes directly to the centre of Warsaw. It might be the best option for you, because you don't need to change from bus to train like in case of "Koleje Mazowieckie".
You can also use trains provided by "Koleje Mazowieckie" railways. To get to the station from the airport you need to take a bus in green-yellow-white colours of "Koleje Mazowieckie". It has bus stop in front of the terminal and goes directly to the "Modlin" railway station. Then you have to take a special train to Warsaw. Here you have more details with pictures
One more possibility is TAXI. Here are listed recommended companies with phone numbers and price list in PDF file (this list is in Polish - it depends on day and distance, but you will pay around 200 zł).
You can also try to use BlaBlaCar and reach Warsaw by carpooling! If only you are able to match time and free slot you will get to Warsaw fast, comfortable and cheap.
Use following link to find offers:
Just enter in search "Mazowiecki Port Lotniczy" which is a valid name of Modlin Airport in Google Maps