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?
You can use special bus "Modlin Bus" - http://www.modlinbus.com/ It has a bus stop in front of airport terminal and goes directly to the center of Warsaw. Maybe it is 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" company. To get to the station from airport you need to take a bus in colours of "Koleje Mazowieckie" company. It has bus stop in front of terminal and goes directly to the "Modlin" railway station. Then you have to take special train to Warsaw. Here you have more details with pictures
And 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 about 200 zł).