Usually our first contact with someone is from a distance.
We use our eyes to see how others respond to us, to watch for danger and look for opportunity. Eyes actually relay an incredible amount of information subconsciously to other people. Watch for sustained eye contact from the person you are interested in. If you glance at her, and catch her glancing at you, you are on the right track. Women tend to look at a man, then look away or lower their eyes, then look back to see if he is catching the signals. Also, when women are attracted to someone, they tend to open their eyes a bit wider and to blink more often.
Be alert to how and when you are near each other.
When a woman is interested, she will usually find ways to be near you. She will choose a seat by you, think of a question to ask you, or find a need for something near you. When a woman is interested in a man, she will get a little closer to him to find out if she should pursue getting to know him.
Pay attention to subtle body language.
See if she tends to lean in toward you, or position her body in a more open stance toward you. She might point her knees or feet toward you. When a person is interested in someone of the opposite sex, she might touch her face or her own body. She might touch or twirl her own hair, touch her neck or smooth and tend to her clothes. This is a subtle suggestion that she would be open to touching, or being touched by, you.
Be aware of subtle sexual displays.
She might lean in to allow a bit more of a view of her breasts or stretch and arrange her legs to attract your attention to her body. A woman will call attention to her hips and waist by putting a hand to her hip or emphasizing the sway in her walk. Subtlety is key here. If a sexual display is too overt, the signal is desperation or insecurity.