There is a traditional code of conduct that civilians tend to follow when meeting members of the British royal family, though they are technically voluntary. These rules include performing a subtle bow or curtsy and referring to the person with a formal title of respect. The title "Your Majesty" should only be addressed to the queen, while all other members may appropriately be called "Your Royal Highness."
The appropriate titles include "sir" for male members of the royal family and "ma'am" for female members. Typically, these terms are to be used after the civilian has already once referred to the individual as "Your Majesty" or "Your Royal Highness," depending on position.
People tend to voluntarily adhere to this code of conduct while meeting the royal family, including world leaders. This code of conduct also holds that, aside from a handshake, which the royal must offer first, people should not touch members of the royal family unless they're touched first, which generally doesn't happen. This is so rare that the news media pointed it out when Queen Elizabeth touched American First Lady Michelle Obama on the back as a friendly gesture in 2009.