Begin by taking down some notes about yourself. Highlight your interests, activities and any important moments in your personal life. Note any great moments in academia that inspired you as a person, or note any personal moments that inspired you to further your academic career. Make sure to isolate a few points that you'd like to discuss with the admissions team. According to College Board, these points should be revealing, detailed and personable. If the topic has been designated by the college, make sure to keep this in mind.
Research the school to which you are applying---make sure your research is thorough. You don't want to apply to a program that doesn't exist or talk about a feature the school doesn't have. Make sure your cover letter reflects the school's important features. Isolate one or two interesting points about the school to tie into your essay.
Start the cover letter by introducing yourself to the admissions team. Hook them with a vivid first sentence about yourself. For example, you could write something like, "I knew I first wanted to become a doctor when I saw my next-door neighbor fall and break his leg." This is an interesting hook that lets them know your academic passion is unique to your personal experience.
Expand on your opening statement---in the case of the example, the accident. Explain your feelings during the incident and why it has made an impact on your desire to go to medical school. Use personal experiences with lively details to tell a story about your life in general. Tie this into your academic interests by highlighting what you want to study and why it is important to you and to society.
Detail how the school to which you are applying will help you succeed in your future. Point out the features you researched and let the admissions team know how this will be helpful to you personally or professionally.
Edit your cover letter carefully. Have a teacher or professional proofread your work for clarity, structure and correct grammar.