I find it very easy to talk to random people, random hot girls, somewhat harder, but still easy for the initial conversation. I used be shyer, then I spent a few months in jail, then my thought process for people on the outside for approaching them became "will this person punch me if I say X to them?" As far as talking to random people, it's more "Just do it" that comes to mind. I made lots of acquaintances and a few friends from talking to random people, plus lots of useful info.
Random people is a good test, as you almost never have to worry about seeing or choosing to talk to them again, so you can be a complete fool and not care I found out. My problem is, especially with girls, they don't read car magazines, or do much of what I do at all, I can't go talk about small block chevys with them or whatever, you know? The other problem after, even if a girl falls head over heels for me, uh, then what do I do?
To me, random people are the easiest, the hardest thing is small groups, as there's a group dynamic of sorts that has to be worked with, to fit in, but be an individual at the same time. Big groups, random people, hell, I'll prolly never see them again anyway, so I now lack fear in that regard.
So yeah, to put it shortly, just do it, and for me, I just think when was the last time some random dude at a fair or on the street wronged me significantly? Like never. It's mostly "friends" that hurt you the most. Maybe that's a little pessimistic of an outlook, but that's how I talk to random people.
It can almost be a challenge, too, a way to test social skills without getting hurt, seriously, it's very unlikely someone's gonna fight you, and if they say something not nice to you, screw it, you'll probably never be forced to talk with them again. I guess also be friendly and don't be a dick, too.
If only "connecting" with people for real was this easy...