First and foremost, test the waters: Unless the woman you’re after is undeniably attracted to you as well, chances are that your advances will not be welcome. So start off by always saying “hi” to her and smile at her every time you cross paths with her. Doing this frequently will make her aware of you. After you’ve done this a few times, you can progress to trying to extend your interaction with her beyond just saying “hi.” Do not try to pick her up or ask her out at this point. Just keep the conversations on work related stuff or other neutral topics. The purpose of this is to gauge how receptive she is simply talking to you and also to get her comfortable around you and used to talking to you.
Secondly, assuming you now know she has a receptive attitude when you talk to her, it’s time to start joking around with her. By this I mean it’s OK to tease her a little and be somewhat playful here and there. In other words, try to bring out both her sense of humor and yours. I say this because you don’t want to come across as just another boring guy at work that talks to her and only all about business and work related stuff.
Thirdly, now that you’ve established a little rapport with her, it’s time to invite her out for lunch or happy hour drinks after work or any other after hours activity. The important part here is to make sure you invite her to join you and other co-workers. Bringing other co-workers into the picture makes things a loss less threatening to her. Plus, she’ll feel a lot more encouraged to accept the invite since everyone else is going. At this point you’re still going to keep things friendly between the two of you since you don’t want to make any advances in front of other co-workers. It’s OK to flirt a little when you have those opportunistic alone moments with her.
Lastly, now that you’ve both been out of the office together – albeit with other co-workers – the idea of going out with you again some place else won’t seem so foreign to her anymore. A few days later while at the office, invite her to hang out with you one-on-one for lunch or preferably drinks after work. Again do this privately when you cross paths in the office hallway or parking lot or someplace similar. If she accepts, this would be a good time to exchange numbers. If she declines, then politely suggest another time with a smile.