This is the no-nonsense approach. You tell her you want to meet her and go right to doing so. If you use this opening approach you should apologize first for taking the liberty. Examples:

"Excuse me, but I saw you walking by a moment ago (or a while ago) and I decided right then that I just had to meet you."

"Hi! I hope you don't mind my saying hello to you. I've really never met you, but if we waited for someone to introduce us, we would never meet. My name is…"

"You know, I'd like to meet you." (pause) "I wish we were at a party. Then I could come right up and introduce myself." (Pause as if thinking) "I know, let's pretend we are at a party. Hi, my name is ...What's yours?"

"Excuse me, but do you mind if I join you?" If the girl has no objections, this is fine. But if she seems embarrassed and uncomfortable, or if she says "No," you should back off a bit. You can say, "You know, I'm sorry for coming on strong like this. I hope I haven't embarrassed you too much, but I really would like to meet you, and I couldn't think of any other way." This should give her a chance to reconsider. If she doesn't invite you to join her then, you can try a little small talk and then ask her again.

With all these examples you should be ready with some "filler" talk to kill any awkward silences until the girl accepts the idea of your approaching her.