In general, from what I've seen, guys usually don't get the girl they have a fixated crush on, probably b/c of the aforementioned pressure and inclination to start acting weird. It happens, but usually not. Your mind gets all strange and it is like a "Something About Mary" situation. Also, like guys, girls often have a type of guy they like, which is beyond your control. So, she might like guys who are taller or shorter, lighter or darker, buffer or skinnier, or whatever than you are. No amount of plotting is going to make you her type if you already aren't, so might as well find out.
In general, I'd say the grand gestures don't work. Showing up at the local hangout spot with a dozen roses and reciting a poem has the potential to be awkward, put her on the spot, embarrass her, etc. Don't make a spectacle. Plus, women like confidence and when you are too fixated on her, you lose that and go into desperation, which is not attractive. Or worse, you seem psycho-stalker.
When you are fixated on one chick, it is tough because of the number of dudes in the world. When you are open to any chick, it is easier, because of the number of chicks in the world.
The best pick-up line is still "Hi." Don't let it fester and build-up into something weird. Put on a decent shirt, some nice shoes, a little gunk in your hair, a very small splash of cologne, and go up to her the next time you see her and say, "Hi." See if you can get into a conversation with her. Read if she is interested in talking to you or not. As was mentioned, don't just blather on yourself, but let her talk. People like to talk about themselves, so get her to talk about herself and ask follow-up questions. I've seen guys blow it with a girl by spending all their time talking to try to convince the girl how cool they are, when they would've been better served by shutting up and letting her get a word in at some point. Compliment her once on something, but nothing too obvious or dramatic. Like, don't tell her she has beautiful, soulful eyes. No, tell her you like her necklace or her nail polish or shoes or something, something that you do actually think is cool. See how she reacts. You should be able to tell from chatting with her whether she has any interest or not. There are signs. Eye contact is good. Smiling is good. Her asking you questions is good, shows she is interested in what you think. If you say something funny and she touches your arm when she laughs, that is a great sign. If she gives a one word response to every question you ask while looking away, that is not a good sign. At this point, all you've done is struck up a conversation, so you haven't really lost anything. If it seems to be going alright, ask her if she wants to do something with you sometime, in a way that shows you are interested in her, but won't be devastated if she says 'no' to you. Get it over with. If she says 'yes' then cool. If not, then you can work on getting over her and finding a girl who does want to hang out with you.
. I would literally post some pictures of me and her if I'm successful, or just make it my new Avatar.