Recognizing the friend zone
Your first concern is to know the difference between being in the friend zone and being a possible romantic interest for the girl in question, but this is often pretty difficult if you don't know her very well. Pay close attention to how she interacts with you and how she allocates her attention. Do you often find her making eye contact across the room? Talking to you more than other guys or being generally more amorous around you? If so you are probably already well on your way to getting out of the friend zone and you should consider making a move.
But chances are if you're having trouble leaving the friend zone it means that she isn't giving you these sorts of cues, so you'll have to take action yourself. However, before you consider trying anything, you need to weigh your risks and think about the implications of your actions.
Risking the friendship
There's a certain amount of flirting you can get away with, but if you take things far enough you run the risk of making the relationship awkward and tense if things don't work out. That means you have to weigh the significance of your friendship vs. the possibility of a relationship, taking into account the chance of her being interested in you (no, it's not 50/50).
So just how much do you value your current friendship with the girl you're after? Would it be a major loss if you stopped talking or hanging out together? If so you really want to know what her reaction will be before you make your move. Remember, it usually doesn't matter how you express your feelings for her for the first time, she already has her mind made up and she knows if she's interested in you or not. That said, it's up to you to get to know her and carefully read how she acts around you to determine what her answer will be.
Letting her know how you feel
This is usually the hardest step for guys, it's difficult to let a girl know you're interested in dating her without being blunt, but too much subtlty is exactly what gets you in the friend zone in the first place. You have the find the sweet spot with your flirting, be clear enough so that she knows you like her but not so much that things are awkward.
A good way to do this is to just ask her to hang out sometime, just you and her doing something fun. If she makes an excuse and doesn't follow up with another time you can go or something else you can do, she's probably not interested.
It's hard to tell sometimes whether a girl considers you a really good friend or a possible romantic interest, a lot of girls have no problem watching movies and hanging out with a guy all the time without any intention of taking it to the next level. Sometimes you just have to take the plunge and risk the friendship if a relationship is really what you're looking for. There have been plenty of successes with just leaning in for a kiss and hoping for the best, but you should ideally start a little bit slower.