Try to find out how serious she is about the person she's dating. Are they dating casually? Or are they in an exclusive relationship? The easiest way to find out is to be direct: "Do you have a boyfriend?" or "Are you single?" If she says she doesn't have a boyfriend, or that she is single, just ask her out normally. Just because she's gone on a few dates with someone doesn't mean she can't go on a date with someone else.
If she's in a relationship, one thing you can do is be bold and ask her if she's happy. Or, ask her if she loves him. If you sense any hesitation, ask her out, making sure to let her know you won't overstep boundaries:
Another approach is to give her your contact information, telling her it's just in case she becomes single. Skip straight to giving her a way to contact you: "Here's my number. If things don't work out between you and that guy, call me and I'll take you out to dinner." If she's loyal to her relationship, or simply not interested, she'll throw your contact information away. But if she's interested, and her relationship is on the rocks, she might get in touch after they break up and you've done no harm just trying.
Take great care to steer clear of the friend zone. Just because she's in a relationship doesn't mean you can't make your romantic intentions clear, or else you might become the brotherly shoulder she cries on whenever there's trouble in paradise. Continue to remind her that you want to date her, you don't just want to be her friend (that is, you don't want to wait in the wings). And if she seems to be stringing you along, for example, she says she wants you around, but she stays with her boyfriend nonetheless, move on. Unless you're content being someone's backup, don't put yourself in line for being hurt; realize that even if they do break up down the track, she might decide "I don't want to ruin our friendship" or she just might want to be single for a while.
Avoid becoming a side dish. If she seems to really like you, demand that she break off the relationship before you do anything with her. If she cheats on him with you, not only is that pretty low on your part, but that brings her entire trustworthiness into question. And if she seems willing to cheat on her boyfriend, you might want to reconsider whether you want to be in a relationship with someone who's ready and willing to violate someone's trust, because next time it could be you at the receiving end of her unfaithfulness.
