I avoid writing walls of text but this is kind of a milestone for me.

tl;dr: It went like shit. I can only imagine it being worse if someone filmed the whole thing. But I'm glad I did it!

So I was at the library cafeteria taking a lunch brake from my studying. The place was pretty packed. I sit at a table and across me in a corner I notice this absolutely stunning girl sitting alone, writing something and smiling while typing something on her cellphone. So while I eat my lunch I notice she glanced at me a couple of times, which definitely helped me summon the courage to go talk to her.

This is when I realized how big my anxiety problem was. I've had a girlfriend before, I've been probably to 20+ dates, but I never approached a beautiful girl like this in a crowded place in daytime. While I'm debating myself what to do, I feel my heart rate go waaay up and I'm starting to get really nervous.

I finish my lunch and say what the hell I'll try it. I go up to her and immediately she makes an awkward face like she's thinking:"oh fuck". I blurt out: Hi, my name is blabla, would you like to have coffee with me sometime? She says: sorry, no. I wasn't expecting such a cold reaction so I was at a loss for words. I blurt out: you have a boyfriend or? She says: yeah sorry. So I just awkwardly leave without even saying goodbye.

In retrospect, things I did wrong: I didn't stare at her, but when we made eye contact I tried not to avert my eyes, which I would say is a good thing. She probably noticed my hesitation to approach so I ended up being this creepy guy. When I approached I was way to nervous, my voice tone and body language showed that for sure.

Things to improve: Lighten up, practice body language, be less outcome dependant. I'm not sure if anything can help my nervousness and my mind shutting down like it did except more exposure to this kind of stress, so I'll keep on trying!

Any advice for a newb?

Edit: Thanks for all the advice guys. The only info I have is from MMs Models which I really like, but it doesn't explain a lot what to do after you introduce yourself, except that you clearly state your intentions. I will explore the guys you mentioned and the links from the sidebar.