Of the two best friends I have (husband and bffl) I met one irl, and the other online, but the process was relatively the same. They introduced themselves, we started just talking about inane goofy stuff, we realized we enjoyed each others company, and we BOTH started to actively look to talk to each other.
Really the best thing you can do is be proactive. If you want to be friends with someone just go up and say hi! Maybe comment on their art or a book they're reading, just be friendly, and if they're receptive start a casual conversation. Maybe you'll click and from that point friendship will blossom.
The thing I struggled with was just realizing that it isn't the end of the world if I tried to make a friend and failed. Maybe you just don't have the chemistry, maybe they turned out to be kind of rude or just don't want to be friends, either way at least you were friendly and tried. Keep trying, make an effort to not always be the one being contacted (people feel rejected if they're always the only one making an effort), and you'll find someone you work well with eventually. 
