How do I ask her to be my girlfriend?

Well ask her what he likes then do that and see that she happy and than tell her.

Well, above all, take into account the sort of girl you're doing this for. If she's allergic, a dozen roses is not the best call, nor should you pull a shy girl up on stage. Be sure to consider her tastes, and what she'll find romantic above any advice any of us offer. (Asking her friends may also be helpful) That said:

Surprising her with a dozen roses is very tried-and-true (deliver them in person), and gives her something to show off to her friends for the whole week.

If you want something dramatic (and memorable) you could get a couple of your friends to help you perform her favorite romantic movie scene (the bar bit in Top Gun comes to mind), but that requires prep. Work, and is likely to overwhelm the poor girl, particularly if she's shy.

Actually, if you know of any love scenes that struck a chord with her, re-enacting any of those, or just drawing on them for inspiration. (Having a girl who's a Jane Austen lover gives you excellent material).

Poetry is a bit tricky, unless you happen to be good at it, or borrow from the best (Byron, Shelley, Burns, Lovelace, Brennan), but you can always take bits of poems, songs and such, and use them to lead her to you. (Leave the first somewhere she'll find it, then have each piece guide her to the next, and on to you. ) You can leave her little romantic things along the way, or have the trip lead her through places that are memorable to you two.

If you aren't already dating, you could leave her bits of poetry, or heartfelt notes from a secret admirer (over about a week). With the last one, include a place/time and confess to her there. Sunset on the beach is a particularly good time for this.

Oh, and don't wrack yourself trying to make whatever you do excruciatingly perfect. Just do your best; that you put your heart into things will show her more than a flawless execution.

And good luck!

How well do you know her? If you know her relatively well, then it shouldn't be too hard.
you can :
1) serenade her in a song
2) paint her something and write the question on the back
3) good prose or poetry (nothing cliched)
4) get a decent date setting (dinner, walk by the river/beach etc. ) and just ask her