I think a lot of people have the wrong idea about what it means to "fit in". Somehow the phrase has come to mean "becoming like everyone else." It saddens me to see people accepting this false dichotomy between being yourself and being socially appropriate. There's no good reason for anyone not to fit socially into the average small group. You don't have to become best friends with everyone in the group; small group dynamics usually depend more on social skills than on denying yourself and becoming a copycat. A department business meeting, a small classroom, a dinner party, a family reunion--all of these events require small group skills, but none of them would demand that you reinvent yourself in order to be accepted.
A couple of people have pointed out the importance of taking time to observe what's going on. I think that introverts sometimes overcompensate for their introversion. In an effort not to seem stand-offish, they sometimes jump in without taking time to survey the terrain. Don't be afraid to watch for 5 or 10 minutes when you're new to a group. Take it slowly when you begin to interract. If you're not sure what to say, it's okay to wait until someone speaks to you first. There's nothing wrong with being new to a group, nothing wrong with acknowledging that you're an outsider and you don't know all the inside jokes and phrases. They really don't expect you to.
I remember an old Andy Griffith episode about a new guy who came to Mayberry and freaked everyone out because he knew everything about them. He knew their names, where they worked, who their spouses were, when and where the last social event was, etc. He jumped in just like he was one of them. Naturally, people found him creepy and began to avoid him. In the end, it turned out that he was from a big city and just wanted a hometown of his own. He subscribed to the Mayberry paper and studied it for months to learn all about everyone so he could fit in seamlessly when he came--but he forgot to allow time for everyone to get to know him.
The same holds true for any other small group. Give yourself time to figure out what's going on and what is acceptable behavior, and give everyone else time to warm up to you. Offer some information about yourself, as seems appropriate, and show an equal interest in them. Don't flood them with personal stories or lectures about your pet project--save those for close friends. It's generally safe to talk about whatever has brought you together: lightweight business at a business meeting, kinship at a family reunion, subject matter in a classroom. Either way, respect the group and let it lead you.
Ironically, one of the things that often makes it difficult for people to fit into a group is their overwhelming desire to fit in. They become anxious and unnatural, and this feeling is unintentionally but unmistakably communicated to everyone else. It becomes a bit self-fulfilling. The advice to "be yourself" is less about clinging to any tactless idiosyncrasies and more about being calm and comfortable in your own skin.
