You have two main options when searching for accommodation: established student housing foundations and the private market. 

Student housing providers are listed on the SOA (Finnish Student Housing Ltd.) website. The average monthly rent for a single room in a shared student flat ranges from around €160 - €380. 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 might also be a good idea to see if the institution you are applying to has any specific advice on student accommodation. So also check the related information on the website of your hosting Finnish university or UAS.