From the airport:
Zwirki i Wigury is a street that begins right at the Airport exit and it ends practically at the point you need to reach. There are two buses you can take that go practically door to door: 175 and 188.
You need to buy bus tickets in a kiosk at the airport. You will need one for you and one for your luggage (unless it is very small). You activate the ticket by inserting it into a slot of a yellow device in the bus.
If you prefer to take a taxi (for example if you are arriving late at night) the fare should be approximately 15 zlotys (approx. 4 EUR). Just avoid the taxi drivers approaching you in the airport hall - they will charge you more than a taxi taken at the taxi stand right outside the exit.
From train station Warszawa Centralna.
You need to take a street-car going in the direction Okecie or Banacha (they have the direction clearly specified). To get to the street-car stop: if you arrive from Moscow, it is on the left side, if from Berlin - on the right side. You need tickets, like in a bus. You should get of at Wawelska stop. From there the best idea is to walk along the Wawelska street for maybe 200 meters. Then you turn right into Zwirki i Wigury. You will see two ugly grey buldings very soon. The dorm is one of them.
Here is the picture of DOM STUDENCKI