Two Truths and a Lie
A good way to learn about new people is to play Two Truths and a Lie. Go around the group, and have each person tell two true things about themselves and one lie. The rest of the group must guess which things are true and which is the lie. You will learn two interesting things about each person, which you can use as conversation starters.
Interview
Pair the teens up into groups of two. Have them take turns "interviewing" the other person and finding out as much as they can in an allotted amount of time (maybe 10 or 15 minutes). They need to know where the person is from, their hobbies and some interesting bits of trivia about their partners. Then each person can introduce their new friend to the rest of the group. Everyone else can ask questions if they discover something they want to know more about.
Bingo
Everyone will receive a card with squares similar to a bingo card. Each square will have a statement on it such as "completed a marathon," "entered a beauty pageant," "been to a foreign country" and so on. Make this an easy task by creating nine squares rather than the 25 squares found in a traditional Bingo card. The teens must go around the group and find someone that has done each of the things mentioned--you can't use the same person for two squares. Continue the game until everyone gets a Bingo.
Toilet Paper Game
Sit the teens in a circle, and pass around a new roll of toilet paper. Don't tell them how to play the game yet--just tell them that you are going to play a game using toilet paper and to take as many squares as they think they might need. Once everyone has their toilet paper, they must go around the circle and tell one fact about themselves for each square they are holding.