What you should do:
You need a Finnish personal identity code. If you come to Finland for a temporary period i.e. less than one year you may obtain it at the local tax office. You must fill out a registration form to give the tax office the details needed for the Population Register System (for more information, see the beginning of this article).
However, if you stay longer than a year, you must visit the Local Register Office (called maistraatti in Finnish; magistraten in Swedish).
When you visit the local tax office they will give you instructions for filing an application for a tax card. The application form is Form 5042a. Give the tax card to your employer. The employer will then use the rate printed on the tax card for withholding the tax on your pay.
Form 5042a, Application for tax card for foreigners and persons who have been living abroad
If your employer company is not Finnish and does not have a permanent establishment it may not have the obligation to withhold tax for the Finnish Tax Administration. Then it will be important that you ask for the tax office to officially compute prepayments (ennakkovero; förskottskatt) for you. You will then make the prepayments yourself. If you neglect your prepayments and have no withholding, you will end up paying surtax and interest.