So I tried to actually go out and do something today.

I was in the library and saw a cute girl down the aisle of books. I walked up to her, passed her, pretended to see some books (I know, I shouldn't have), and then walked back to her when I saw her taking photos of a book with her phone. I said to her "that's silly, why don't you just check the book out, it's free." and I smiled. She just said "okay" and I walked away.

NOW... after that, I kind of got hyper and walked up to another girl who actually worked in the library. I just asked her "are any of the rooms available to check out?" and she said "okay let me look" and then I said "well I was just asking, maybe for some other time. thanks" and I walked away.

I feel my heart beating faster, I get a little anxiety and just don't know how to keep it cool, calm, and collected. I WANT to try this again some other day but mann - what do I do??

^ WTF? I don't get why you'd even do this.

You've just got some approach anxiety. Everyone gets it. I still have it sometimes - I think everyone likely does, to a point...

Only way to get past it is to approach, approach, approach. Just talk to people... say hello to people on the street... You need to get comfortable talking to people, then you need to get comfortable FAILING. You'll get rejected. A lot. (I can't count the number of times I've been rejected... it would probably be thousands)... You learn to not really care about it... and you'll discover there's actually no physical pain involved - and your game will only improve.

You'll get better and better the more you do it. You'll figure out what works and what doesn't.

So - go out, approach 20 people today... Just talk to them.