Ok, so I'm new to this whole thing and I've read plenty of things on this website and others, but I've never really practiced or opened/talked to a girl.

So... Friday I was standing waiting for my food from Taco Bell at the food court when I noticed this HB7 standing next to me. It took me a while but I just decided to say something to get over my AA so I just commented on how Taco Bell takes forever yet McDonalds (right next to us) was a lot faster despite its longer line. She replied and we talked, she laughed, I commented on something she had written on her hand, blah blah usual stuff.

Anyway, I was judging how much time I had left by going by the numbers being called out (you get a number after ordering your food). Then suddenly he called out 2 numbers, then ~20 seconds later another 2 numbers (one being hers) so she went to get her food and said "well it was nice talking to you".

The problem is, I didn't number close or even introduce myself! The conversation was going well so I forgot about telling her my name.
So, my question is... how can I introduce myself if there's no pause in the conversation? Do I just randomly say "I'm ______ by the way"? Or should I ask for hers instead?
Also how can I number close? I felt like it would have been awkward to try to n-close this girl I just met and talked to for a few minutes.

Oh, and if I happen to see her again on Monday, how should I approach? Just with a "so i see you decided to eat at [whatever place] today?" ?

Any help/comments would be greatly appreciated!

Speaking of introducing yourself... It is common courtesy to introduce yourself on this forum before starting writing posts...

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I'm not trying to be a dick Ezo, but you're being a Pick Up Snob in my opinion.

bbardot: you just reminded me about porn

Sorry about that.
Before I registered on these forums I was telling myself I need to introduce myself on here before I get started (I have been browsing these forums for a while), but I guess I just forgot.

So, can anyone help me with this?

When the conversation is going well you can drop your name like for instance "hey I'm x btw" and reach out your hand. She will reply as we're programmed by society to.

But rather than introducing yourself you should've taught about how well the conversation went - did you get some IOI's? - and then possibly just went to sit opposite or next to her (depending on the way the chairs are positioned.)

Sounds good, thanks! That's what I figured you would just do but I wasn't sure if there was a smoother way to go about it doing it.

I'm not too sure about the IOI's. My main reason of even talking to her was just to talk to a girl and try to get over that AA. She laughed and smiled a lot, but that's about all I can remember right now.
Oh, and I don't remember what brought it up but she mentioned that she was sitting with some friends that are waiting on her. Otherwise I would have sat with her.

I saw her again today on my way to class. I smiled at her and she smiled back but I was in a hurry so I just kept walking.
Should I approach her again the next time I see her? If so, how should I start it off?

Oh it's you again. How's it going?
Will be a solid start.

Anywayz about the smoother than smooth introductory: don't try to be too slick. It's lame and girls will think you try to hard. Saying your name and reaching out for a handshake will be smooth enough. Anything more will overdo it.

Alright, thanks for all your help.