Identify flirtatious behavior. In the workplace, a coworker has a number of unique opportunities to show that she likes you. Leaving abundant notes for you at your desk or around the office could be a sign of affection, especially if she signs them with love. She also is likely to be flirting if she asks you to lunch frequently, sits by you at every meeting and buys you coffee at every opportunity.
Talk to other coworkers to find out what they know. The advantage to a workplace romance is that you will have mutual friends. Get to know her friends around the office. When you feel you have their confidence, ask them if she has feelings for you.
Watch how she treats other male coworkers. Some girls with an outgoing personality will flirt with many different men without meaning anything by it. Check to see if her attention is exclusively fixed on you or if she is merely a flirtatious person.
Examine the motivations behind her flirtations. If you work in a mundane environment, she may just be trying to make the workplace a more interesting place to be. If you are her superior, she might be trying to get a raise or promotion. Determine if there may be any other causes for her attention before making a move.
Discuss the situation with her. This step should be done with caution after you have carefully observed her behavior and thought the relationship through. Keep in mind that you will continue to see her at work every day. Avoid any confessions that might cause embarrassment if you have misread her flirtations. Most girls will appreciate an open conversation. Your honesty is sure to lead -- if not to a romance -- at least to a closer relationship with your coworker.