The most important point about introductions is to make them. If you have ever been left standing there not introduced, you know what I mean. Most people would rather you introduce them incorrectly than to be left standing there unacknowledged. The second point in introductions is the order of names. Knowing the proper way to do this allows you to make a good impression.  This order differs for business and social situations.

BUSINESS INTRODUCTIONS are based on power and hierarchy. Persons of lesser authority are introduced to persons of greater authority. Gender plays no role in business etiquette and introductions.

For example, you would say, "Mr./Ms. Greater Authority, I would like to introduce Mr./Ms. Lesser Authority." The name of Greater Authority is spoken first.

SOCIAL INTRODUCTIONS are based on chivalry, so introductions are made according to age, then gender, and then social status. The man is introduced to the woman unless the man is obviously a great deal older, in which case it's "age before beauty." For example, if both people are of the same generation, you would say, "Mary Smith, I'd like to introduce Bob Jones." But, if the woman is considerably younger, you would say, "Mr. Smith, this is my daughter Agnes."

When introducing relatives, mention their relationship to you; it avoids any possible faux pas. "Mark, my husband, or Kate, my wife." If a couple is living together, but not married, introduce both by their first and last names; no other information is necessary.

If you do forget someone's name, do not say, "I've forgotten your name." It makes that person feel unimportant. Take the blame by saying something like "I've drawn a blank. Please tell me your name again." Then make the introduction and get off the subject of the memory lapse. If someone forgets your name, just jump in, hand outstretched, a smile on your face, and offer your name. 

Remember this: manners, especially in introductions, are more noticeable in their absence. Gracious introductions put you and the people you are introducing at ease. Good manners take you above and beyond the average person; they make you stand out as a person of class and grace.

 Portions taken from article by Gloria Auth, Protocol Plus, www.protocolplus.net.

"You can make more friends in two months by becoming interested in other people than you can in two years by trying to get people interested in you." -- Dale Carnegie Charm does not consist of impressing other people, but of allowing others to impress you. "The hardest job kids face today is learning good manners without seeing any." -- Fred Astaire