Include all of your personal information at the start of the letter. You should include your full name, student ID number, current address and phone numbers and email address.
List the courses you are currently taking as well as the courses you intend to take if your appeal is successful.
Explain the situation with which you have been dealing and connect it to your schoolwork. You have to make a strong case for why your circumstances had a negative impact on your ability to focus on coursework.
Talk to the head of your specific department if the courses in which you had trouble are related to your major. He should be able to send a personal evaluation of your plan and abilities to your school's appeals committee.
Explain what you have done and are currently doing to rectify your academic situation and get your studies back on track.
Include any important documentation you can find that backs up your claims, such as notes from a doctor or therapist.
Submit your appeal to the appeals committee and continue your studies as usual until you receive a response. This process can take a couple of weeks, depending on your university.