Hey man, let me start off by saying I know exactly how you feel.
When I was in high school, there was this girl who I was mad in love with. We had a few classes together which opened up chances for me to talk and become friends with her. One day I asked for her email and we would chat a lot nearly everyday.Everyone liked her, she was very sociable and sweet.
We would go out occasionally together and talked frequently, this went on for a year.
Now here is where our stories differ; after a year I decided to express my feelings of wanting to be her boyfriend. She had told me no, that she doesn't share the same feelings I do. Despite that, we remained friends as usual for another year. After 2 years, we got into an argument and stopped talking for a bit. I did the mature thing and apologized and told her that I care too much about her to not be friends. So after a third year of being friends I told her again that I love her once more and finally this time she accepted.
In the last months of high school we were a couple and went to prom together. A year after graduating our relationship is stronger than ever and we have a very passionate relationship. In all it took me 3 years to get the girl :)
I'll give you advice from my experiences and mistakes I made. Follow these 3 suggestions and things should work out a lot better.
First of all, don't give up! If you really love the girl you will be willing to fight 'til the end for her. Having an attitude of " I know that it will never be...She wouldn't go for guys like me" is giving up before even trying. Worst approach possible. You need confidence my friend, girls like confidence (not cockiness). The fact that she is popular changes nothing at all, stop thinking it does. So keep making your progress to build your friendship and this time have a mindset that your doing this to get her. Remember, confidence!
Second, find the right balance in your approach! By this I mean you have to spend the right amount of time with her. If you talk and see her rarely, she won't think there is anything happening between you. On the other hand if you are always asking to talk to her and always trying to spend time with her and always complimenting her, she will think you are obsessive. An easy way to achieve the right balance is by being interested in whats going on in her life (ask her about family, school, activities she does) and following up on her. This will show you are interested in her in a caring way. Also try to have the same circle of friends, it will make you relevant. Remember, quality time together is better than a large quantity!
Third, and probably the hardest, is to get the courage to tell her how you feel. Once your relationship is healthy and active, ask her if you could talk about something together. Do it when you guys are alone, like you said you go out together some times. In that moment tell her how you feel: you think she's "the best girl in the school. She's beautiful, funny, nice and you really care for her. You love her." Say you want to be her boyfriend and get to know her more. Maybe she didn't know you felt like this or maybe she had been waiting to get this kind of response from you. You have to let her know you love her. Remember, be honest and open about your feelings!
Now I can't predict what she says. If it's a no, don't take it as an insult or as the end of your chances. Some girls just aren't ready to date yet, others may say no just out of nervousness or because they are shy. If she does say no, ask her to give you a chance to show her you can be a great boyfriend, then if it's still a no give it a rest for that day. Pretend she never said no and keep making the progress you were before asking her out. She will pay more attention to you after she knows how you feel. If it's a yes well congratulations, don't lose her!
These things take time. It's the same if she does say yes; it will take some time before you can kiss her, and it will take time after that before you can touch her. Remember though there's nothing wrong with moving on if you feel it's taking too long. I know with the girl I wanted, giving up just wasn't an option, I needed her. But it's all up to you. So patience, there's no rush.
My last bit of advice is to not close your eyes to the fact that there are other girls.I know you feel so strongly about this girl you are interested in that you believe no other girl is as good nor better than her, but it's not true. Keep a lookout for other girls, you might just find a new favorite. I'm not saying to be a player, but rather to notice qualities of other girls as well. The only time you should be concentrated on one girl is when you are dating or married.
Best wishes to you my friend, I hope you get the girl of your dreams like I did.
YES, it is possible for you to get this girl, and NO it's not just in movies.