While good, lasting romances have started in the workplace (as stated above), woe be to you if you get into a relationship and you break up or get really serious. Sometimes it makes for a really awkward situation in the workplace, because somehow others will know.
That said, I’ve gone out with co-workers, but always kept it a friendship level. Rumors flew, but that didn’t bother either of us because we both knew we were just friends.
As others have said, take it slow and let it progress naturally. See if chance meetings in the hall are more than “How are you?” and if she eats in the lunchroom, arrange to coincidentally be there too.
Also, keep in mind that most people are nice to the IT guy/gal, because you’re doing something for them, and they need your service. I’ve known IT staff who put those who annoy them on the bottom of the ticket list when possible.
A few big Don’ts.
Don’t spend more than a few minutes chatting in the hall or anyway else. You’re both there to work and neither of your managers or co-workers will appreciate your taking time away from work. Remember that every minute you spend together is 2x the work not being done.
Don’t ask her co-workers about her. That’s just creepy and may be considered harassment.
Don’t assume she’s single and ready to mingle. I once almost asked a manager (who would chat me up) out to the movies. Turns out she was the owner’s girlfriend!
Don’t make it obvious, especially to your IT co-workers that you’re really interested in her. IT staff generally know and visit just about everyone in the company and they may inadvertently let it slip that you’re interested and rumors may fly. May not bother you, but it may bother her.