Find an opening. If you want to introduce people to each other, then it's important to get the timing right. You don't want to to end up having blundered before the introductions have even begun by introducing the wrong people to each other or by interrupting a fantastic conversation just to get the details out of the way. Here's what you need to know:
If you find yourself in conversation with two people who don't know each other, try to introduce them as soon as possible. This can get a little tricky. Let's say you're with your college roommate, Amanda, when you run into your friend from high school, Jake, who launches into a story about a mutual friend. Poor Amanda will be standing there feeling awkward and bored while Jake rambles on. It's important to find an opening so that you can include Amanda into the conversation.
You should avoid introducing someone to people who are in the middle of a serious conversation. Maybe you're at a work event with a client, and you've been eager to introduce him to your boss. While this is an important introduction that should be made, you should avoid doing so if your boss seems to be entangled in a deep conversation with another person. You should wait for an opening, when your boss doesn't seem extremely absorbed; making introductions at the wrong time can lead people to not hit it off as well as they could.