Now that we know how to respond to the invitation, and how to choose what to wear to the dance, it’s time we discuss what to say.
What to Say
Gentlemen, if this is not your area of expertise, I recommend not over complicating this part. Simply walk up to a girl, politely get her attention (say her name, or “excuse me, ma’am,”), and ask, “May I have this dance?”.
Ladies, when presented with this offer, your response should be something similar to, “Certainly!”. If you would rather sit this one out, be straightforward, and say something like, “I’m not dancing this one, but thank you!”.
What Not to Do
Gentlemen, unless she is your wife, do not ask the same girl to dance multiple times in a row. In some settings, it’s best not to even ask the same girl twice in an evening! But, use your judgement here. You do not want to monopolize her evening, and (if the ratio of ladies to gentlemen is as it usually is) you want to give other girls the opportunity to dance.
Ladies, do not refuse to dance with one man, then accept the offer of another man for the same dance. If you especially want to avoid dancing with a man who has just asked you, you may politely decline (as stated above), but you should sit out for that whole dance. This is more honorable and considerate.