Fellas, when it comes to pursuing that young lady who makes your heart beat faster simply by thinking about her, keep in mind that you should always act like a gentleman. I can speak from experience that participating in crazy antics simply to show off will look exactly like you trying to show off and will likely not be impressive. Instead of jumping off of the roof to show that you can do so without hurting yourself, engage in conversation so both of you can get to know each other better. And remember that her friends and/or sisters might hang around, so be willing to engage them in conversation, too. How you interact with her friends and family, especially when you don't know she's watching or listening, will go a long way toward demonstrating what sort of person you are.
Another thing to be careful of is pushing too far and too fast. My wife and I met through eHarmony and exchanged regular e-mails and a couple of phone calls during the first six weeks before we met in person. When we did meet, it was connected with a two-day Home School Alumni gathering at someone's house in Wisconsin, about 45 minutes from where my dad lives. She, two of her sisters, and I met at Pizza Hut before going to the house to have dinner and make the initial meeting away from a bunch of people I wouldn't know. When we got to the house, several of us played games for an hour or two before it got to the point that I needed to get some sleep (I was working the night shift at the time, and out of nervous excitement over the meeting that day, I didn't really sleep at all). I had been told I could sleep at the house where the gathering was being held, but I had already planned to stay at my dad's so I wouldn't make Abi any more uncomfortable. We actually didn't speak much during the entire weekend, not until about the last hour or two Saturday evening before I needed to get back to my dad's to sleep, but during that time we were observing each other (and not in a creepy stalker way).
When I got back to my home and we started e-mailing again, one of the first things Abi told me was that she wasn't sure of her feelings for me. At this point, I could have pressed for a decision and pushed her away in the process, decided that I wanted someone who knew better after a month and a half of communication and ended things myself, or continued communicating in a non-threatening way after letting her know she could have the time she needed to make up her mind. Thankfully, I picked the third option. We had already made plans for me to visit her family three weeks after our initial meeting, and while I would have been willing to give her more time beyond that, seeing how I interacted with her family helped her make the decision that she was willing to pursue something more serious. Eight weeks after that was the next time we were able to see each other, and this was for a week-long trip to Wisconsin to meet some of my friends and family. Eight weeks later we were officially courting, ten weeks more and we were engaged, and after a final four months we were married, about twelve and a half months after our first e-mail exchange. The timing of all that wasn't really pertinent to the point I was making of not pressuring the lady of interest, so please don't look at my relationship with my wife as some sort of timeline your own relationship should follow; some people need more time, some less.
Finally, what if the young lady or a member of her family tells you she isn't interested in a romantic relationship? My advice is to back off. You don't necessarily have to disappear from her life, but don't get your hopes set on something happening. If you were friends with her before you made your thoughts known, you can still be friends, but, as was the case when I expressed interest in a friend of mine, she may need space for a little while. You might need the space, too, in order to clear your mind. This is not the time to try and butter up her friends and family so they will tell her what a great guy you are, but it is the time to demonstrate that you can handle such a rejection gracefully.
However, if the only context you have known this woman has been centered in romanticism, it might be better to simply walk away. About a year before Abi and I started communicating, I met someone else on eHarmony. Looking back, I had little discernment in that relationship, and things were progressing a lot faster than was wise, especially since this woman and I were not on the same page. We were in steady contact for about two months, most of it romantic in nature, before she decided that she didn't see me as anything more than a friend. That was a huge blow to me because I was very emotionally invested, and I had a terrible time letting go. I spent the next two or three months in considerable contact with her, trying to get her to change her mind. This was a bad idea, in large part because I think she liked the attention and didn't do much to push me away. Because we didn't have a friendship in the first place, it would have been wiser for me to have accepted her decision and broken off contact. That is sometimes necessary, so if you are in the position where a woman has told you she isn't interested, be prepared to walk away.
The old saying that when one door closes another one opens is true. But it doesn't always work the way we want it to. If a relationship ends, that doesn't necessarily mean another one is waiting right around the corner. What it does mean is that you've just been given the chance to learn a lesson and you should take advantage of that.
Okay, this post feels like a ramble, but hopefully my thoughts are somewhat clear. There may be more to follow on this topic in the future, so stay tuned! (I know you're just gripping the edge of your seat in anticipation.)