This is how I did the one for my librarian position. I hope it helps.
Dear Person Hiring for this Job,
I am writing to ask you to consider me for X position. This is a paragraph about why I want to do X position in general. It includes at least one personal detail and at least one job skill I consider a particular strength. It argues that I am passionate about this career. It is not long.
I have had the opportunity to gain experience in this job by - paragraph about my work or study experience. It should go from most recent experience back. Include some details about your responsibilities/achievements in your most recent or most important positions. If you have mostly study experience, give more detail about what exactly you studied. If you shadowed people, mention that. If your work experience is largely unrelated, try to shoehorn some of it in (e.g. I gained experience working with people by). You can supplement with relevant hobbies. (But if you do have recent, relevant work experience, you should largely be detailing that. Only embroider the other stuff if you need to flesh it out.) This should be the longest paragraph.
I hope you will consider allowing me to do X thing at your company. This is a few sentences about why I want to work at your company in particular and what I think I could bring. Try to mention at least one detail from the company website, so they know you visited it. This is a short paragraph that parallels the first one.
Thank you very much for your time and attention.
Sincerely,
Person You Would Be a Fool Not to At Least Interview