There are many landlords in Helsinki to which you can submit a housing application. For example, Sato, Vvo and Avara own rental apartments in Helsinki. Also, insurance companies, banks, and many private persons offer rental housing. You can find housing also through a private landlord for example on Vuokraovi.com.
Normally, the city-owned rental housing is more affordable than privately-owned housing. However, there are a lot of applicants for city-owned rental housing and only a small number of applicants receive housing. You can apply for rental housing owned by the City of Helsinki online through the City apartment service.