The word “present” is preferable on formal occasions to the word “introduce.”
On informal occasions neither word is expressed, though understood, as will be shown below. The correct formal introduction is:
“Mrs. Jones, may I present Mr. Smith?”
The younger person is always presented to the older or more distinguished, but a gentleman is always presented to a lady, even though he is an old gentleman of great distinction and the lady a mere slip of a girl.
Do not say: “Mr. Jones, shake hands with Mr. Smith,” or “Mrs. Jones, I want to make you acquainted with Mrs. Smith.”
Never say: “make you acquainted with” and do not, in introducing one person to another, call one of them “my friend.” You can say “my aunt,” or “my sister,” or “my cousin”—but to pick out a particular person as “my friend” is not only bad style but, unless you have only one friend, bad manners—as it implies Mrs. Smith is “my friend” and you are a stranger.
Do not repeat “Mrs. Jones? Mrs. Smith! Mrs. Smith? Mrs. Jones!” To say each name once is quite enough.
Most people of good taste very much dislike being asked their names. To say “What is your name?” is always abrupt and unflattering. If you want to know with whom you have been talking, you can generally find a third person later and ask.
Best Society has only one phrase in acknowledgment of an introduction: “How do you do?” It literally accepts no other.
When Mr. Bachelor says, “Mrs. Worldly, may I present Mr. Struthers?” Mrs. Worldly says, “How do you do?” Struthers bows, and says nothing. To sweetly echo “Mr. Struthers?” with a rising inflection on “—thers?” is not good form.
Saccharine chirpings should be classed with crooked little fingers, high hand-shaking and other affectations.
All affectations are bad form.