Canadians' Royal bow
See the photo demonstration.
Address all correspondence to "The Private Secretary of Her Majesty the Queen," not the queen herself. Request that the correspondence be communicated to her royal person.
Contact the queen at the following address: Her Majesty, Queen Elizabeth II, Buckingham Palace, London SW1A 1AA, England.
Greet the queen as "your majesty" initially. Use ma'am thereafter.
Accept the queen's offer of a handshake, and, of course, a bit of conversation if she's willing.
Don't show the queen your back, if you're following tradition, and leave the room only after the queen does. But keep in mind that times have changed and formalities have eased.