On the letter its-self be sure to put your address and the date, so that the appeals team can get back to you. Start off your letter in the usual manner if you know who you are writing to, otherwise use "Dear Sir or Madam". Get straight to the point and outline your reason for writing the letter in the first sentence. For example "I am writing to appeal against my academic dismissal". Then move on the detail the evidence in your favour referring to the evidence you have attached (if any). Be sure to note any previous high scores in tests etc. At the end of your letter, write "Sincerely," followed by your name and signature.
Here are some examples of the style of appeals and complaint letters. Read them though to understand what you are aiming for.
www.letterwritingguide.com/sampleappeal.htm and www.letterwritingguide.com/samplecomplaint.htm