I'd like to live with a Polish family instead of taking a dorm room at my uni's campus, and I heard this is one of the options for international students in Poland, so can you please guide me to where I'd be able to find one?
Who told you that? I think that it's impossible. I've only heard about some older lonely people subletting room in their flat in exchange for help with shopping and lower than market price. Actually if you have chance go for dormitory, because they're cheaper than renting something on the free market.
If you want to be close to a Polish family (to learn the language and culture), the best option is to rent a room in their house. It's quite common, but I doubt it would be for free, unless you make some special arrangements as Monitor mentioned. You probably mix it with an international student exchange program where family of each student host them in their own country for a period of time, but it must be an exchange .. two ways, not one way.
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