Couchsurfing is a global community of 7 million people in more than 100,000 cities around the world. 18,000 of its members are registered in Minsk, according to couchsurfing.org.
The members of Couchsurfing network offer apartments to each other for free for short-term stays. An added bonus is that your local hosts will also be your informal guides around Minsk, telling you about their favorite places, meals and people in Minsk. Couchsurfers in Minsk will more likely speak English or other foreign language than ordinary Belarusians in the street.