In addition to Unihome, it's a good idea to also look for housing options from the open market. Here are a few good guides to help you get started:
If you need a short-term place to stay while looking for a long-term flat, the Helsinki area has a number of hostels you can book a room from. Airbnb also lists a wide selection of available flats from private owners. And if you've never tried couchsurfing before, that might also be a fun way to start your Helsinki experience while looking for a more permanent home!
Social media channels (especially Facebook) also have numerous privately operated groups where anyone can advertise rental flats – some just for students, some for everyone. A quick Google search will land you a long list of the most popular groups.
Furnish your apartment
Most of the student rooms or apartments are rented unfurnished. There are numerous furniture shops in the Helsinki metropolitan area – Ikea stores, for example, are a good option for affordable furniture and other household items.
Buying second hand is also a great option for super affordable, sustainable furniture shopping. For example Kierrätyskeskus ("Reuse centre"), a not-for-profit company dedicated to recycling furniture, clothes and other household items, has several locations in the metropolitan area. The locations vary in size and selection: if you're looking for large furniture like beds and sofas, choose one of the biggest centres.
You may also want to search local recycling groups in social media for affordable second hand furniture.