p/s/a: Going up to a girl pretty much anywhere in public and saying something like "I thought you looked cute and wanted to meet you" actually works if your body language is in order. If this seems too scary, going on Chatroulette or Omegle and being vaguely interesting also works, and I know people who have gotten married from meeting this way.

Probably already accounted for by the use of the word "girl" rather than "woman" here, but I suspect this depends on the age of the lady in question (and on the age of the man, for that matter).