Approach the person with whom you wish to dance.
Catch the person's eye. If he or she is engaged in conversation, wait within earshot of the conversation and break in when appropriate.
Say, "Excuse me," when appropriate. Do not introduce yourself - save that for the dance floor.
Hold your hands down. Do not offer a hand.
Ask, "May I have this dance?" or, "Would you care to dance?"
If the dance is accepted, offer your arm.
Proceed to the dance floor together.