Do I need to have a social security number in order to register myself into a library in Finland or I only need to provide an address where I am living?
The user regulations may vary from one library to another, but at least here in HelMet libraries (Helsinki Metropolitan Area Libraries) it is not necessary to have a Finnish social security number to get a library card. You only have to have an address in Finland and present a valid ID card or passport. If you do not have a Finnish social security number, your library card will only be valid for six months at a time. After that period, you have to visit the library to renew the validity of the library card.
Check the user regulations at http://www.helmet.fi/search~S9/ -> Help -> User regulations.