International exchange and degree students are allowed to work in Finland with certain restrictions. The restrictions have to do with the nationality (EU/EEA or non-EU/EEA) and the nature of employment. In addition, the regulations for study-related work, compulsory training or employment having to do with thesis work tend to be more relaxed. For postgraduate research work, the regulations are vaguer and must be checked from the local employment office.
If you are a Nordic or EU/EEA national, you do not need any special permits for working in Finland during your studies. There are no restrictions on how many hours per week you are allowed to work, but you should take care that work does not get in the way of your study progress.
Non-EU students can work within certain limits on a student residence permit if the work is practical training included in the degree or if the amount of part-time work does not exceed 25 hours a week. There are no limits in terms of hours on full-time work outside term times (summer and Christmas holidays specifically). For general regulations on working in Finland, see intofinland.fi.