WARNING! Large post coming up! If you want to do this with tact, you better read it all, buddy.
Well, joking aside: it's pretty simple, really...
You don't ask her out... Yet...
In order to avoid potentially losing her as a friend and making things very awkward between the two of you, you'll first have to figure out whether she's really interested in you.
You can do this pretty easily:
1. move closer to her (when sitting on a chair for example), turn towards her, lean in to whisper something to her.
2. touch her. A casual touch on her wrist when making a point or when laughing in conversation. Or when she's sitting somewhere with her back turned to you and you walk up to her without being seen, gently touch her shoulders when greeting her.
3. TOUCH HER! But this time, do it 'romantically loaded'. When talking, just stop, or stop listening when she's talking (i.e. shift focus completely to her hair or mouth), and then try to touch her more intimately, like stroking some hair behind her ears, or touching the side of her lips when there's some food or moisture stuck there or something. Hugging her tightly (5 seconds or more) when thanking her.
And then WATCH HER RESPONSE. WATCH HER RESPONSE WATCH HER RESPONSEEE!!!!
If she backs off or if she looks like she's saying 'get him off me!' in her mind (even if it's slightly), you'll have some work to do, because she doesn't feel comfortable around you being so touchy-feely, and she probably isn't very interested. If she seems receptive, on the other hand, when she smiles and looks you in the eye, when she blushes or (ideally, of course), when she touches you back, then you're probably on the right track.
Now, one final note: I want you to do this presicely in that order - do not suddenly start feeling up her lips when you haven't touched or been remotely close to her physically before, it'll just be creepy - and don't do it in machine-gun tempo. Easy, cowboy, you have the time. You should ideally do this over a couple of days.
One more warning: if she seems unreceptive to your advances, then don't persue it. If she doesn't like you being closer to her than you normally are, then don't touch her (yet, there's always a way to turn things around). If she doesn't like to be touched, then don't go lip-smearing (yet). Honestly: you might still stand a chance when you take things slow and stop when she wants you to stop (even if she doesn't say it verbally), but when you're being all creepy and pushy, then it's game over for you.
Now, there are other ways to find out whether she's interested in you, of course, but this is the simplest, most effective, most 'unromantic' (that is: you don't need very much skill in romance, tact, or romantic/sexual conversation to do this).
A'ight?
Great! Report back in a couple of days (or less) when you've done this.
Or, if you want to quicken things up, you can pop the question about you've really posted this thread about when the tension is high between the two of you.
If you brush her hair back, she seems receptive (and ideally, of course, when she's appearing to be shy, shyly smiling, or blushing, for example), just ask 'hey, I just remembered, I'm gonna go to the cinema [or shopping or whatever you want to do] this weekend, wanna come with me?'
And again: watch her response. Look at her bodylanguage, her tone of voice, the way she looks at you.
And again: report back once you've done all this. Report your every move, and her every move, in as much detail as possible. And don't forget to look at this stuff objectively. Do not get all subjective when observing her, if she backs off, she backs off. There's no 'but' here.
Mmkay?
See you then! Cheers and good luck!
-RB