Thank you everyone, I've been following this discussion and trying to absorb as much before saying anything more. I think the tone is getting a little uncivil, and would prefer it to remain respectful. We all have had different experiences in dating, and that can skew how we approach it and the advice that we dispense.
I've spoken to all my close female friends about dating because I like to get their advice. In the past, my personality has been to be more aggressive when it comes to dating, which sometimes has worked out but more often didn't. I instead went to the reverse, thinking that would be better, and it also didn't work. I realized only about a year or so ago in a previous relationship was that it wasn't exactly my approach that failed, but rather my inability to gauge what my date wanted and what she was feeling before making a move. Of course, my approach makes a big impact on how my date views me, but if I don't take her thoughts and desires into consideration, there can be little happiness. I may not have worded the past sentence perfectly, I'm not very good at expressing myself in words, but in short, I need to listen more and talk less.
Among my female friends, there is near consensus that they feel that the guy should take the lead in most cases. They expect a guy to ask them to out first, that they shouldn't be the one initiating the first date and that if they do so, they feel that the guy won't ever take the lead. Personally, I do like it when a women asks out a guy. I don't know if the person I am seeing feels the same way, but in our past conversations, it is clear that she comes from a traditional background, so there's a large probability that she feels that I should be taking the lead. I think this past Sunday at the museum worked out well, I didn't throw my hand around her, but instead put my hand lightly on her back and gauged her reaction. If she didn't seem at all uncomfortable, I would have withdrawn my hand and avoided contact. When she reacted positively, I didn't try to press her further, but allowed her to make the next move, if she was inclined to do so, and to my delight she did so. We held hands as I walked her to her car, which amusingly was parked right next to mine. I gave her a hug before saying goodbye and she hugged me back fairly heartily. I believe that if I had tried to lean in for a kiss, she would have reciprocated. It's possible that she wanted me to kiss her.
I'm more worried now about seeing passive in her eyes. I don't know her dating history, nor what she is looking for in a guy, but I do feel confident that she does like me and would like to spend more time with me. I'm perfectly willing to wait to kiss her for the right mood, but feel that she was looking for me to kiss her on Sunday, or on our last outing(when we were food packing for a charity). I don't really feel comfortable asking her, "I would like to kiss you, may I?," though perhaps many of you are correct in that she may love hearing that.
I've invited her to my friend's New Year party and she is willing to go, she's nervous about being around people she doesn't know. Thankfully my friend's party is going to be a mix of games and general hanging out, which is putting it at ease (ie, she won't need to just stand around talking to people she doesn't know or staying by my side and being introduced to a ton of people). I'm an extrovert and she's an introvert, so this is understandable. She hasn't offered to invite me to any of her friend's parties, but I would be willing to go. If we don't see each other for NY, then I plan to ask her out to dinner this weekend, I want to wait to talk to her about NY before planning further. If she does come to NY, I hope she will have a good time. Maybe she'll be looking for me to kiss her when the ball drops, maybe not, but I'll do my best to gauge her interest and body language before I lean in for a kiss. Either way, I just want to spend more time with her to get to know her better.