Make a group introduction correctly. In this case, you will need to spend a little time introducing the newcomer to each individual of the group unless it's a small, informal group where a general introduction would suffice and it's neither time-consuming nor disruptive to name each member of the group while you have the group's attention.
For more formal, larger groups, introduce the newcomer to the whole group first, then take the newcomer to each person and introduce by name: "Caroline, this is Fitzwilliam, my boss; Lydia, this is Fitzwilliam, my boss," etc. Continue working your way around the group in this manner.
Though you may think it's funny or just easier to say, "Mary, this is everybody. Everybody, this is Mary," this doesn't actually help get a conversation going. Besides, it's rude to "everybody," because it makes it seem like you don't think it's worth it for Mary to get to know each person. Of course, use your discretion: if you're at a loud party and Mary just got there, it may be overwhelming to introduce her to twelve new faces immediately. Instead, ease Mary into the conversation and introduce her to a few people at a time.