Americans do not tend to be very clear on the meaning of European titles and their ranks and meanings, but if you have occasion to write a letter to a Countess, you are writing a letter to a woman who has a high rank in European aristocracy. A Countess is a woman who is either the wife or widow of an Earl or a Count, or a woman with the equivalent rank of an Earl or Count herself, in the case of an inherited title.
Begin the letter by typing your address. Skip a line and type the date. Skip another line and type "The Rt Hon.The Countess of (place name), followed by her address. Do not insert her actual name in the address, only her title.
Skip another line and type "Dear Madam" followed by a colon. Again, do not include her real name because the proposer protocol is to refer to her as "Madam."
Type the rest of your letter as usual. If you do not know the Countess personally, maintain a respectful and formal tone that is befitting to her royal station. Even if you do not personally revere her for her title alone, if you wish to be polite and adhere to the proper protocol you must treat her with formality and respect.
Conclude the letter by typing "Yours faithfully," skip three lines and type your name. Print the letter and sign your name above the typed name in blue or black ink.