<human>: So after weeks of talking to this girl in one of my classes, I asked her if she wanted to "hang out" last night. We agreed to meet up to get pizza and I'd meet her by her dorm.

I got ready,  put on nice clothing, cologne, showered, the works. I meet her by her dorm at the agreed time, and she shows up in workout clothes and is  fresh from the gym. I know I don't have much experience, but I have enough sense to know the no girl dresses like that on a first date. I figured that I'd do my best with what I got.

She seemed taken aback that i paid for her, but Dinner went well, we held good conversation, I minded my manners, etc. I also found out more  about her and that she's a cool person who fits my type. 

After dinner, we walk back to her dorm, and I notice she had some closed body language (crossed arms, but it was a little chilly too I guess) despite the fact that dinner went well.I made sure to keep my hands out of my pockets, but to not make a move, except for the end. I read on an article that on a first date to always end it with a handshake, hug, or a kiss. So remembering this, I at the very last second went in for a handshake. I'm still cringing from how awkward it was.

I know that the expectation is to text her within 24 hours of seeing her (that's what the Internet says at least) but I don't know if I should, and if I do what to say. I still want to see her, and my end goal is a relationship. Please help.

Can you condense the text into a few key points?
<bot>: I thought a hangout with a girl was a date, it wa a nt. It went well, but awkward me decided to end it with a handshake. What should I text her/say?