You have two main options when searching for accommodation: established non-profit student housing organisations and the private market.

Student housing providers are listed on the Homes for Students website by SOA (Finnish Student Housing Ltd.) . The average monthly rent for a single room in a shared student flat ranges from around €200 - €400. Single apartments or family flats are also available, but the rent is likely to be higher in these non-shared apartments and they often have long waiting lists. 

You can also arrange housing independently by searching for rented flats on the open market, or on social media. Open market flats tend to be more expensive than those available via student housing foundations. 

It is also a good idea to ask the university you have been admitted to for advice on the other locally available student accommodation alternatives. Check the related information on the website of your Finnish university or UAS.