If you are a citizen of EU/EEA member state, Liechtenstein or Switzerland you do not need a residence permit to stay in Finland. You can stay and work freely in Finland for up to three months as long as you have a valid passport or National identity card.
Non-EU citizens must first apply for a permit to work or conduct business in Finland. If you are currently in your country of residence, apply for the permit at a Finnish embassy or consulate. If you are currently in Finland, submit your application to the Finnish Immigration Service (Migri). You cannot proceed further until the permit has been granted.
If you are staying in Finland for over three months remember to register your right of residence with the Finnish Immigration Service, Migri and register your place of domicile at your Local Register Office to ensure that your details are entered in the Population Information System. Everyone registered in the Population Information System is given a personal identity number that is used for health care, taxation etc.
A visa is an entry permit for a short, temporary visit of less than 90 days. If you are a non-EU citizen you might require a visa to visit Finland and a valid passport or some other travel document accepted by Finland. It must be valid for at least ninety days after your intended date of departure from the Schengen area.
For more info on visas please refer to Ministry of Foreign Affairs of Finland.