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How should I ask her out? (casually)? 3 questions

Okay, so I am 21 and she is 19 (let's call her Sierra). I met her last October for my friends (Kevin) 21st birthday, his sister invited Sierra (Kelly). I really liked her, she was really cute and down to earth and spoke her mind. Well, I talked to Kevin about it, who in turn talked to Kelly about it. She approved because "I am a good guy." So, they have set up (in the past) for the four of us to casually hangout to see if we would get along. This happened twice over the course of a few months. Kevin and Kelly both believe that I did well and have a chance. I too believe that I did well on both occasions. Now, we are all about to get together again and things will probably go well, and if they do, Kevin and Kelly are going to leave the room and I will ask her out. I have never asked out a girl before, never had a girlfriend, She has never had a boyfriend either. I am feeling very confident that we are hitting it off (along with approval of Kevin and Kelly). So, while I feel confident, I have never asked anyone out before, I do not know what to say, like I literally do not know what words to use. I just want to casually ask her out, to get to know her more. I don't want to ask her to be my girlfriend yet, as we still don't know each other all that well. I want to hangout with her more and get to know her, I want her to know that I am interested in her romantically, just that I want to go slow in the beginning. I am going to ask her out no matter what though. She is a big anime fan, so she is not like regular girls but frankly that just makes her better to me. Please Help me, thank you!
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Age (I would really like help from those 18 through 25 but am willing to take any help I can. No one younger than 14 please)
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My question is in the details above. But the short version: How do I casually ask her out? what words do I use? And any other thoughts you may have?
This poll was created on 2015-04-24 00:31:59 by NONtoxic