Since we, in the USA rejected the idea of royalty leading us for over 200 years, we are a little rusty on protocols on meeting, greeting and dealing with royalty.
So I did some research to help us ignorant yanks re-accustom ourselves with royalty and how to act.
the Prince (or Princess) is initially addressed as "Your Highness," and the King (or Queen) is initially addressed as "Your Majesty." Then, in subsequent conversation, "Sir" or "Ma'am" are used, with an occasional repeat use of "Your Highness/Majesty." The familiar "you" must not be used. The title "Ma'am" is NOT pronounced "marm," as some will have it; say, "ma'em" smoothly (two syllables gives an artificial Southern accent to the word).
When in doubt, the generic "Sir" or "Ma'am" will serve until the correct address can be ascertained. However, don't wait too long. If you wish to know a person's rank or title, simply ask. Furthermore, if you have forgotten a name, simply ask. You will not be thought rude. Nobles and Royals, like everyone else, also suffer from "name slippage," so if you can repeat your name in your conversation, that action will be much appreciated by others.
THE BOW/CURTSY FOR A ROYAL
The term "physical courtesy" means the bow (for men) or the curtsy (for women). Where a curtsy is not possible for the woman, as, for example, because of age or infirmity, the bow is substituted. You bow/curtsy to the Head and Chief of Arms of a Royal House and to the Head's spouse. The bow or curtsy is not exaggerated and does not call attention to it. Physical courtesy is done once upon being introduced and once upon leaving the Royal presence. Do not offer to shake hands unless the Royal offers a hand first. Generally, elected officials of the U.S. Government who are representing the U.S. government at an event and active U.S. military members in uniform who are representing the U.S. government at an event neither bow nor curtsey to Royals, but do shake hands when the Royal offers a hand. Elected officials and military persons, when not acting in official capacity, may bow or curtsey to a Royal.
GIVING THE BOW
A slight bow by the man is made from the waist while the head bows and the eyes look at the feet of the Royal. For lesser Royals, only the head bows and the eyes look at the feet of the Royal. The bow is not exaggerated, but is dignified and given smoothly and with quick deliberation.
GIVING THE CURTSY
The lady curtsies by placing the ball of the right foot behind the heel of the left foot, with the feet at a natural and comfortable angle to each other to maintain balance; simultaneously, the hands are crossed at the breast and the head is bowed slightly while the entire body is slightly "dipped" at the bent knees. The curtsy is not exaggerated, but is dignified and given smoothly and with quick deliberation.
Visiting Royalty to an event sponsored by a Royal House are not in their own Courts and receive a lesser bow or curtsy.
Also Bright Ideas and True Confessions: How and What to Do and Why is a good read about royal "presence."
Tudor King George
Coronation Portrait of King George