If you see a girl at a party or with a group of friends, you can pull one of her friends aside and simply ask if she's single. Don't, however, ask one of her girlfriends if you don't know the friend well; the girlfriend might think you're making conversation because you like her, and then be offended when you ask about her friend instead. Feel free to ask any male friend, but beware that he might actually be her boyfriend. And when you ask, don't say, "Is she single?" Try something more nonchalant, like "What's her story?" so it's not clear that you're asking for yourself.
Social networking isn't just for fun; you can do some serious detective work by checking out a Myspace or Facebook page. Add her as a friend, and then you'll be able to see her "relationship status." However, even if her status isn't posted, you can look through some of her profile pictures or photo albums to see if there is a recurring appearance of the same guy or any kissing pictures. This usually means she's involved with someone.
If you really want to find out if a girl is single and are confident, just ask her directly. The very worst she can do is tell you she's unavailable, and she'll probably feel flattered that you even asked. Begin with some simple small talk about her interests and throw a little humor in. When it seems that you've created a rapport with her, ask her what she's doing later that night. If she's not available, she may say she has plans with her boyfriend. You get the information you sought, and you depart as friends with no harm done.