A combination of school+social events. I'm kind of not very good at making new friends regularly, because I'm basically a hermit living in the woods, and I'm a little bit shy, but when I find myself meeting people with shared interests, I'm usually able to make friends with them.
I went to a Comics and Visual Arts-college, which means that all my classmates there were interested in similar things as I am - art, comics, animation, etc., - so making friends there was easy! And then I've sort of built from there. Sweden is a pretty small country, which means that when there's a comic-con on, I am bound to meet at least a FEW of my old college friends again (even though the rest of the year we live scattered across the country), which is always nice. And they know more people that they introduce me to, and since I usually have a table at these cons, I can strike up friendships/make acquaintances with the people tabling next to me, etc., etc.
Find somewhere you feel comfortable - be it a coffee shop or a comic con - and just try talking to people. I've found that most people are pretty nice.
As for making friends on the internet.... I've found it's, again, easiest to do this with someone who shares interests with you. You won't become super-best friends from the start, but talking regularly helps, etc. I've made most of my online connections either via Twitter or here on Tapastic (Tapastic is, like, the friendliest place <3).