Pretty much what the previous people said. I would start thinking what kind of area you want to do a PhD in, then find out who might be a potential supervisor and contact them directly. They will also be able to tell you whether you really need that NZ master's equivalent degree or your normal Finnish one will be enough (I suspect most would be perfectly happy with that).
As a lecturer I get quite a few emails asking for PhD/master's places, as I am sure your potential supervisor will. So some advice from me:
- please don't write to every single person in a department. We academics actually talk to each other
If I get an email from someone who appears to be suitable, but in an area in which a collegeague has better credentials, I forward it and so do my colleagues. One day I got about 6 copies of the same email, one directly sent to me the other 5 via different colleagues. It makes you look very desperate, usually not a good sign!
- select the potential supervisor carefully and make sure that at least on paper they look like the best fit for what you would like to do. Sound obvious, but I have had requests for PhD's rangeing from plant physiology to economics (I am an irrigation engineering in a civil engineering department....), again makes you look desperate, still not a good idea.
- include a scan of your transcipt with a list of courses. It gives us academics a quick idea of your background and lets us quickly identify where there might be gaps in your knowledge. I personally don't find the grades particularly interesting, but plenty others do, so include those.
- if you submit your own proposal talk about why you think a particular research needs doing, how does it advance your area of study? "I like to study the shape of doorknobs" makes me groan whereas "The shape of doorknobs is an important aspect in the determination of the age, social status and colonial influence of the British Empire of residential properties and therefore can be used as one tool in the preservation of the heritage of our country" make me think that you have thought about it a little bit (actually I personally think doorknobs are not particularly interesting, but you get the idea
Anyway that's my 2 pennies worth. Hope you will get around to doing it, it can be very frustrating, it will be an obsession, but it is definitely worth it. Good luck in advance!
HTH