If you want to stay in Finland for a longer period than three months, you need a residence permit. (Nationals of an EU member state, Iceland, Liechtenstein, Norway or Switzerland do not need a residence permit to come to Finland.)
You can apply for a residence permit in Finland if you have a job, a study place or a family member in Finland. Apply for a residence permit before you come to Finland.
For more information and instructions on how to apply for a residence permit please visit Migri.
Read more here: Guide for students | Maahanmuuttovirasto (migri.fi)