Some apartment buildings might offer free or inexpensive internet connection between 2 and 20 mb so you should ask about this when making your rental contract. This is because they might have their own reliable landline coming in. So if your landlord offers the connection, you just need to buy your own router and turn it on after plugging it in a special socket.
If you wish to get a faster connection or your apartment doesn’t have it’s own internet you can buy those from other providers. Pay for used data subscriptions have pretty much disappeared in Finland and almost all contracts are with unlimited data. The three biggest internet providers in Finland are Elisa, Telia and DNA. From all of them you can get a wireless internet connection and they might throw a free router in the deal. Just be careful when making the deal that you don’t end up with a deal that lasts years. Price for internet varies between 9,99 and 49,99 euros per month depending on the speed and bandwidth.