Hello,
Congrats on your marriage. If the Turkish spouse is currently living in Finland, then you can go to the nearest Turkish embassy that serves the Finland area as well and pay a certain fee and provide some documentation and the embassy will send your info to Turkey and your marriage will be registered there.
Maybe you can even do it this way even if the Turkish spouse does not live in Finland. To do this go to
www.e-konsolosluk.net and go on "evlilik" and then "evlilik tescili". There is an English version too.
Or else, you should go to the Nufus Dairesi/Mudurlugu the Turkish spouse is registered at and provide some docs like your marriage certificate.
If the marriage certificate is in Turkish, does that mean you guys got married at the embassy? If so, that embassy should be able to help you with registering your marriage.
I am looking into the residence requirements myself so if I see anything useful, I will let you know. In any case, the Finnish spouse need a visa to reside in Turkey. Again the above website and the nearest embassy can help you with that.
All the best.
DnT