The people that will read your letter of intent are busy people. They're in charge of bringing students in who can academically perform. They set program requirements, then receive applications from applicants that meet those requirements. Your application and letter of intent gives them the first hint of your interest in their program. They have many letters to review; your job is to get them to read yours and choose you. Your goal is to convince the reader to accept you into their school.
Look at the school's entry requirements for the program you want to write a letter of intent for. If it's a letter of intent for matriculating there, match their qualifications with your experiences. For example, if the school you want to enroll in requires you to have a 3.5 or better GPA, and your current GPA is lower, then you shouldn't write a letter of intent for that school.
Brainstorm experiences that match the school program you're applying for. Organize these thoughts into the following categories: Academic experience, job experience, volunteer, extracurricular and personal experience. Make sure these are related to what you're writing a letter of intent for. For example, if you're trying to go back to school after being suspended for academic performance, focus your letter on things you've done that proves that you've overcome your weaknesses. Then brainstorm experiences you have that prove that you can successfully complete the school's program.
Copy and paste the school's "letter of intent" instructions to your draft. Base your outline in this format; address the points they want you to make in your letter. Write the letter in business letter format, starting with the letter's date, followed by a line space, followed by the reader's name and address. This information is available with the instructions.
Continue the letter by professionally greeting the person, or people, that will review your letter of intent. Skip a space, then introduce yourself and state why you're writing to them. Follow with a statement of why you'd be a good candidate for what you're writing your letter of intent for.
Present the "proof" that you meet the university's standards for the program, or decision, that you're hopping to get approved for. Draw on the information that you brainstormed in Step 2. For example, if you're applying for a management program, and you're a senior in high school, explain how you've used management in your extracurricular activities and your after school job. If you're trying to get reinstated, tell them about how you've overcame the circumstances that held you back the last time. Use a related personal experience that proves that you can continue your studies. Use your experience to demonstrate how you're going to excel with their program. Conclude the letter by thanking them for reading your letter, provide them with your phone number, and let them know that you'll be happy to answer additional questions.
Different schools will have different "letter of intent" requirements. This article provides a general outline of what you'd find in any letter of intent. Be sure that you follow your school's "letter of intent" writing guidelines and requirements.