Since this is a professional letter, you should be sure to use a business letter format with both their address and your own on it. If possible, your letter should be on a letterhead, but it isn't required. Make sure the letter is typed in a standard font (Times New Roman is a good choice) in size 12 font. You should address the letter to a person. Use a name. Yes, more than one person will read your letter, and no, the human resource admin might not be the one calling the shots when hiring, but they are the first ones to see your letter. So, if you cannot find out who is the one with the hiring power, address you letter that person in human resources.
Once you've started the body of your letter, be brief. A cover letter should be a page or less, so make the most of what space you have. This is not a place to rehash your resume; they have copies of that, and have likely already read it. Still, you need to introduce yourself and state that you are a candidate for the position of whatever job you are applying for. If it is customary to state your credentials or schooling in your career field, you might consider briefly doing so in this first paragraph. Then, in the next one or two paragraphs, what you do need to mention is two-fold. Talk about you- and talk about them.
First, even though you aren't going over all the bullet points in your resume, take a moment to explain what skills you have that set you apart from the crowd. Share experiences or abilities that might not have been easily categorized to put onto a resume. Or, maybe there are things on your resume you feel might get overlooked that are especially unique or pertinent. For example, I spent two summers teaching English abroad. Such an experience provides a lot of unique skills, and insights but just looks like another line on a resume, so it always gets mentioned in a cover letter. When sharing these skills and experiences, use dynamic language with action verbs, and don't just say they will make a difference, show your potential employers how with an example.
The other thing you absolute must do- is to show not just what makes you a good fit for the job- but that the job a good fit for you. This means doing your homework, and researching beyond what the job description says, to find about the job and company or institution you are interested in working for. Mention what inspires you about them, or what skill you have that will be of use. It shows them that you don't just want a job, you want this job. Employers would rather have someone who is excited to be there- and one who will hopefully stick around in either the position they are hiring or working their way up at the workplace.
The last paragraph should be brief. Make sure to state how to contact you (you might just consider saying contact information is in your resume, if you prefer), and say you are looking forward to discussing how your skills will be a benefit to them. It is always a tricky to keep from sounding too confident or not confident enough. Implying there will be an interview or phone conversation in the future usually works for walking that tight-rope. Lastly, make sure you thank them for their time and consideration before closing with a respectful benediction like "Sincerely." Make sure to leave space to sign your name (yes, sign, not print!) in black or blue ink, and below that have your name, first and last, typed out along with any other pertinent information (such as if you are an MD).
Hope this helps- and to all you job seekers- good luck!
Further Reading:How to Write a Cover Letter By Alison Greene