Zielone Mazowsze is a hostel owned by a enviromental NGO. Nice place and very cheap, just 35 PLN. It's the closest hostel to Warszawa Centralna Railwaystation. If you don't mind that you cannot stay in the hostel between 11am and 5pm, this is the place to stay! Reception open from 5pm to midnight. uł. Nowogrodzka 46/6, +48-22-6217777, online booking.
Jump Inn Hostel is a little bit out of the center but still in good location. Nice place. Prokuratorska 2, +48-22-8251167, office@jumpinnhostel.com
Hostel Kanonia is directly next to the market square in the old town. uł. Jezuicka 2, +48-22-6350676, hostel@kanonia.pl, online booking.
OkiDoki is between the cultural palace and the old town. Plac Dabrowskiego 3, +48-22-8265112, online booking.
Garden Villa is outside the center in a quiet area. uł. Dolna 42, +48-22-8411173, hostel@gardenvilla.pl, online booking.
A good source of information is Warsaw In Your Pocket.
As not everybody is speaking English in Poland and as you don't want to feel stupid by not even knowing how to say 'Hello' in Polish, print yourself a copy of the Pocket Talk English - Polish micro dictionary.