Take a look here
and at similar sites. You just google 'nieruchomosci' - that's real estate. You want 'na wynajem' to rent and you're looking for a one room apartment 'jeden pokoj' that's how a studio is usually described in Poland. Sometimes it's called a 'kawalerka'. Apart from the rent, there's usually an additional service charge called 'czynsz' which can be an extra three or four hundred zl and will cover cold water, rubbish collection and sometimes electricity and heating bills. I know somebody in a 35sq metre apartment in Warsaw who paid 170zl for his electricity bill last month. His place is all electric, heating, water everything.
This site is also very useful for working out living costs: