How do I overcome my nerves when I see her? What should I say to her?

There's a woman who I sometimes see when I take the train. I've seen her 6 or 7 times, twice in the last week. She's beautiful! Not just a regular kind of beautiful either, there's something special about her. She is, to me, quite literally breathtaking. She seems quiet and to herself, like I am. The last couple times I've seen her, I started telling myself "This is it, just talk to her. Introduce yourself. Say something!" (well, honestly, the first thing I said to myself was "Oh sh*t! There she is!). All to no avail. I just froze up, paralyzed by nervousness, and the fact that that nervousness might lead me to say something stupid. And that's my problem; even if I can bring myself to speak to her, I don't want to say the wrong thing and screw it up for myself.