How do I go about getting into a relationship with this girl?

This is going to be a long post, so brace yourselves. Last week, my aunt, uncle, and cousins came to visit for a few days. They were staying with friends that moved from where they live. Said friends now live close to me. Since they were staying there, my family ended up going there to play games, and what not. One of the girls in their family caught my eye, we'll call her Sam. Anyways, at first, since she didn't really want to play any games, we didn't interact very much. But then, we ended up playing a game that she decided she wanted to play, and she ended up on my team. It was a game called Wits and Wagers, and even though I didn't know most of the answers, I am very good with odds and probabilities, so I ended up winning the game for my team. Throughout the whole game, she was complimenting how smart I was, and what not (I'm not trying to sound like a braggart.) Then we all decided to go get shakes, and it just so happened that I ended up in shotgun in her car. She let me be the "DJ" and we ended up singing along with every song. At one point, she leaned in towards me, and told me that she was going to brake check to freak out the kids in the back (which was hilarious). I felt like we were already really good friends. Then when we got out, and got shakes, maybe because everyone else was there, but she was reserved, and was mainly on her phone for most of the time. When we left, and got back in the car, she was back to her fun self, singing and being funny. When we got home, we played a game called Ghost in the Graveyard, and we pretty much stuck together, at one point she even told me to come hide with her in her room. We had a blast, and I have a pretty big crush on her now. I told my mom that we should hang out with their family more, even though our relatives are no longer in town. Problem is, I don't have her number or anything, so the only way to see her again will be to go to their house. But what I'm wondering is, how do I go about trying to become friends (and hopefully more) with her? Do I ask for her number? I guess I just don't want to screw this up, so am really unsure of how to do this. She doesn't have a Facebook or a Twitter, she only has a Pinterest. I don't have a Pinterest account, and don't know how it works, but I think it would seem weird to make one just to friend/follow her. What do I do? And, if the only way to see her is if my family goes to her family's house, how do I ask for her number or whatever privately? From what I've said, do you think she likes me? Well, once again, sorry for making such a long post, but this is a big deal to me right now.