Dear Mr president, or prime minister, which ever is the case, would be the opening that would be used. then it really depends on what capacity you are writing in, as to how formal the letter should be. For example are you representing a community or a club, or company?
If so you would write your address at the top left hand corner of the page, and then below this on the right side of the sheet of paper, before the body of the letter, you would write the presidents full title, and address. For example,
The President of the United States of America,
The White House,
Capitol Hill.
To end the letter you would use the formally ending, for example
Yours faithfully,
John Smith,
President of the Rotary Club.
If so you would write your address at the top left hand corner of the page, and then below this on the right side of the sheet of paper, before the body of the letter, you would write the presidents full title, and address. For example,
The President of the United States of America,
The White House,
Capitol Hill.
To end the letter you would use the formally ending, for example
Yours faithfully,
John Smith,
President of the Rotary Club.