Finland Visa

Finland is among the Schengen countires and in order to get there you have to apply for a visa. For EU citizens there is no need for the visa, they can stay in Finland for an unrestricted period of time. They also do not need passports; national ID will be enough. Your obtained Schengen visa will be valid in all European countries that are included in the Schengen area. Among the Schengen countries are Austria, Belgium, Czech, Denmark, Slovakia, Slovenia, Spain, Sweden and Switzerland, etc.
You can apply for a Schengen visa to Finland at the embassy of Finland in your country. There are Finnish Embassies worldwide, however if there is not one in your country then you should apply for visa in another Schengen state that represents Finland.

Note that the citizens of the USA as well as Canada, Australia, do not require a visa while traveling to Finland either for business or personal travel but you should also note that the visa is given only for 90 days period. The USA citizens will need a valid American passport to enter Finland.

Residence Permit

For working or studying purposes in Finland foreign citizens have to get residence permit. However this rule does not extend on the EU citizens.
Nevertheless if their stay exceeds the period of three months then they must register their right of the residence in Finland. Non- EU citizens  need residence permit for a long stay in Finland (study, business). The residence permit is issued by the Embassy of Finland in your native country. Residence permits are given on different bases: study, employment, self-employment, family ties in Finland etc.

A residence permit is usually granted for a one year period. But if you have resided in Finland for a continuous period of four years then you will be able to get a permanent residence permit.