Where the hell does one who has no connections get some? I don't live in America, however, there must be some basic strategies that work everywhere, right?
I walk through parts of my city regularly where I am often approached in this way, even though I don't want to buy anything from them. So I only know about the first part, I don't know anything about any transactions after that would take place, or how to keep yourself safe. Maybe dressing like a bum will make the chance they'll mug you smaller.
Alternatively, associate with someone who most likely has some underground connections. Call and meet a prostitute, approach a group of youths hanging around on the street, approach people in a clubbing area, things like that. All of this I got from watching Law and Order but it seems reasonable enough :)
Another thing I forgot to mention, strangely enough, is the internet. There must be forums that discuss drug use in Finnish. They may not post phone numbers but it can't be that hard to find a guide to your local underground market.