How can I start talking to a stranger?

Next time you see her, casually glance over. When she looks at you, catch her eye and flash a smile then nod. She will be thinking about that for the rest of the day. Then any time after that you could get away with going up to her and asking her a question. It could be anything from "what's up" to a cheesy pickup line. She'll laugh, but know you're actually interested.

Just walk up to her. Ask her about her day and her interest. Start talkin.

I think in this case it would probably be best to just go up to her and start conversation.
nothing too drastic - just a simple "hey, how are you - I've seen you around, I can't believe we've never spoke before. "
don't think about it too much; simplicity is often the best way - chances are, if you've caught her looking at you she probably wants to talk but doesn't know how. Just take a chance.

Take a chance! what have you got to lose? my boyfriend walked up to me in an airport when we were waiting for a flight and just said hi how are you? next thing I knew we were sitting talking the whole way home on the plane and we went on our first date the nest night-2 years later were still together. And even if you cnt quite work up the courage and approach her at least smile-maybe she will take the hint? good luck!

Just go up to her and introudce urself there is no better way to getting to really know her that way she knows who you are it s a risk but go ahead take it.

It's simple walk up and say hi I noticed you were checking me out the other day so I decided to come over and say hi I promise I don't bite hard and if nothing else we can be friends