Approach the woman you want to ask out in a confident manner. Self-confidence is an attractive trait and an important part of making a first impression, according to relationship expert and author Dr. Stuart Fisher, in the article, "Ways to Radiate Self-Confidence on your First Date," on eHarmony.com. Smile, be upbeat and make direct eye contact with her when you see her.

Look for a receptive response. If she looks at you as you approach without turning away, or if she smiles slightly or looks at you with some curiosity, it is a good sign that she is open to speaking with you.

Smile and make a respectful gesture to her. Bow your head slightly as you approach her to show deference for encroaching on her space and interrupting whatever she is doing.

Introduce yourself and compliment her. You might tell her she caught your eye the minute she walked in, or that you've seen her here often and noticed she was reading a book from your favorite author. The compliment can be anything nice, but not too cheesy, and it gives you an excuse to approach her.

Check her body language. If she smiles coyly, tilts her head towards you, turns her chair to face you, giggles or lowers her voice slightly, you can bet that she is responding positively and just may accept a coffee date with you.

Be casual, but direct. Don't beat around the bush by asking if she likes coffee or if she has plans later. Just ask her if she wants to grab coffee. For example, you might say, "You want to grab coffee at that new coffee bar on Maple Street?" Asking in a casual manner alleviates the pressures that come with a formal date.

Set specific, but flexible plans. If she says "yes," avoid making ambiguous coffee date plans, such as "sometime next week" or "later this week." Instead, suggest a specific time, date and location. If she can't make it at that time but says she would still love to get coffee with you, ask her what would time work best with her schedule and make set plans. Look forward to a successful coffee date.