Paragraph 1: Introduce yourself if the reader doesn’t already know you. If you already know them, then it is thought to be polite to draw reference in a pleasant manner to the last correspondence or public meeting you shared.
Paragraph 2: State you main reason for writing the letter. You should be as succinct as possible, whilst making sure that you get across all of the information necessary.
Paragraph 3: Conclude your letter politely, asking for some sort of response if necessary, or perhaps by mentioning that you will be in touch again shortly with further news.