Transferring money to and from Finland is not particularly different to transferring money in any other country. Transferring euros is free, for other currencies range of transfer agencies are available for a fee.
Fees on international bank transfers very much depend on how much and what currencies you want to transfer. Bank transfers within the SEPA area should be free while eg. transfers from dollars to euros can cost a lot. For euro to euro transactions use of IBAN (International Bank Account Number) is recommended.
Most, if not all money transfer agencies charge a fee for the transaction. Therefore, for smaller payments, it is probably worth using a foreign card at an ATM or even as a method of payment in a shop. You will probably have to pay a fee for withdrawing from a foreign account, but this fee is almost certain to be less than what you would have had to pay to an agency.
For larger payments, there are international agencies for transferring money, such as Western Union or MoneyGram. Transferring money to and from Finland via these agencies is very simple: The sender goes to an agency in their country, pays in the money and states which foreign agency the money is going to. The receiver then goes to the respective agency, identifies himself with ID and can pick up the money immediately.
However this convenience comes at a hefty price, so you might want to check out other options. In many cases, it is cheaper to transfer money via an online service such as PayPal, Monese or TransferWise, though you need an account with the service in order to do so.