On the back of some Post-it Notes (ie the sticky side), write some good get-to-know you questions. Make sure you write at least as many questions as there are people - you can double up with the questions if there's a lot of people in your group.
Stick them all on a whiteboard or wall so people cannot see the question on the back. Each person then has to come up, pick a post it note and answer the question on the back.
Once done, they select someone else in the group to pick (and answer) the next question.