Write your address at the top right corner of the paper and the recipient's address on the left (two rows beneath your address). Add the date you wrote the letter just beneath your address.
Include a salutation in the beginning of your letter. "Dear Sir/Madam" is acceptable when you do not know the recipient's name. Otherwise, use the recipient's name along with a courtesy title: "Dear Mr. Jackson."
Mention the purpose of your letter in the introductory paragraph. It's helpful for the reader -- whether a professor or a secretary -- to know the reason you are writing (for example: "I am writing to...").
Divide the points you want to make into three paragraphs. Keep relevant points within the same paragraph. Expand your points, but remember that this is a letter, not an essay, so keep it concise.
Use expressions such as "in addition," "furthermore" and "however" to keep the flow throughout the main body of the letter. Don't just copy your bullet points from the notepad.
Mention additional materials you are enclosing with your letter or any temporary changes in your contact details in the concluding paragraph.
Close the letter thanking the recipient ("Thank you very much for considering my request, and I look forward to hearing from you"). "Yours sincerely" is the most suitable phrase to conclude such a letter, followed by your name and a signature (if you don't send it via email).