Introducing two people is really quite easy. Remember to always give a brief description of how you know each person. This gives the two people something to grab onto and start a conversation.
“Mary, I would like you to meet my neighbour, Sue Smith. Sue, this is Mary Jones my colleague at work.”
Also, when introducing two people, the lesser important person is introduced to the more important person.
“Mr Brown may I introduce John Jones the new junior in my department. John, this is Mr Brown the director of the company.”
Always look at the person who you are introducing and then turn to the other person.
Never say something like: “John, come over here and meet James”. This is a very rude way to introduce two people.
When you are shaking hands with someone, give a firm grip with the web of both your hands touching. Give two or three pumps and say, “hello”, “nice to meet you” or “how do you do”. When the other person says the same to you, this is rhetorical which means you do not answer.
Look the person in the eye when shaking hands and have a pleasant expression on your face. Also, stand front on to the person not side on.