Whether from across the room or across the table, eye contact shows you're interested in the other person. Make sure the object of your affection sees you making eye contact, but don't stare. Be playful and look away, rather than staring at the person, which is intimidating. Smile when making contact as an invitation to him and sign you want to talk to him.
Once a conversation starts, be playful with your touch. Lightly graze the person's arm or back. Avoid sexual touching or holding the person. A light touch will send the message you're interested, while not seeming too forward or desperate for attention. Don't force it; touch the person when it comes naturally in the conversation or situation.
A whole range of body language cues show interest. Lean forward toward the person and, for women, cross your legs in his direction to indicate you favor that person more than others in the room. Try mirroring his posture as a cue you are paying attention to him. Other body language useful for flirting is playing with your hair (again, for women), fidgeting and smiling.
Many people feel comfortable talking about themselves, their work or their interests. Ask questions to show you are interested in her, but also remember to actually listen to her response. Active listening, shown through nodding, verbal cues and follow-up questions, shows you are tuned in to her conversation and you are interested in her more than anyone else. It makes people feel important and, in turn, want to spend more time with you.