Introductions, The Correct Form
Proper introductions aren’t exactly a simple matter:
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 […] No lady is ever, except to the President of the United States, a cardinal, or a reigning sovereign, presented to a man.
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.
One has to be wary of inflection, and things get even more complicated when you have to actually shake hands.