But this is shyness, not that they would do it to be rude. We are extremely introvert and unsure. Now some Finnish people may say that I am generalizing, but it really is true. And this is what we are and this is why we are so special.
So, how to make friends with Finnish people:
How to start
Finnish people love dogs, but they behave like cats. So, usually Finnish people want to be the ones that come to you. If you are super social, like Americans or Australians, you might get only bad look without an answer.
If you try to be friend with a Finnish person by smiling to him/her every time you meet, it's not a good thing either. Especially girls will say "what the fuck that one idiot is always smiling to me, he doesn't even know me!"
So I would just say that: ignore a Finnish person as long as you can, they come to you. This might take time, but after this you are going to be good friends!
Don't ever get too cheesy
Finnish people hate cheesy. Especially French guys behavior doesn't work here. If you say cheesy, a Finnish chic say: "A FRENCH GUY!" So, if you are a French guy and trying to meet a Finnish chic, don't be so French.
My tip is that you go to a girl, stop like 80cm away (so don't ever get too close) and... now this is the trick: look at her, deep in her eyes, and ask something stupid like "do you know where I can smoke here"
and then just thank and walk away. Don't look behind.
Why do you do like this? Because first a Finnish girl thinks "oh my god, that guy is coming to talk to me, what a jerk" then she thinks: "that idiot is totally going to try to score me, not in a million years" and then when you only ask where the smoking place is, she's gonna think "what the fu*k, why wasn't he interested of me!" And you might actually get the girl like this, because next she's going to come and talk to you in the smoking area asking where are you from..etc. So this is ignoring.
When we are drunk you can make good friends with us - for one night. Next day we don't usually want to see you anymore. Making friends with drunken Finns is not ideal way. Making friends with a little bit tipsy Finnish is better.
Making friends with a bartender
I used to work in a bar. We had so many people coming and knowing us by names. But for us they were customers. Sad part was that they though us as friends. I would never ever spend time with my customers on my free time. So, you can try to make friends with bartenders. They are usually social and kind - but only when they work. Don't forget that they are getting paid for talking to you.
Spending some time
Helsinki is small. Super small. Everybody knows someone who knows someone. So if you finally make friends with one Finnish, you have a good opportunity to make several others!
Finnish people care about you, but they don't say it every day. If they say it once - it means it and we don't feel like saying it all the time. After we have said it once, it has been said and don't expect to hear it soon again.
Especially in Helsinki it is very hard to make friends, but as I said, once you make friends with a Finnish person it means a good friendship. Usually female are more social than dudes.
Making friends in the street
Not in a million years. Don't ever think you can make friends with a Finnish person like this.