Cover letters are more common in postdoctoral and job applications than in traditional grants for academic research and writing, but occasionally required by some funding agencies. These letters must be formal, meaning that it behooves you to pay attention to form: print on letterhead (make your own if you cannot use your department’s), and be sure include the date, funding agency address, date, a formal salutation, and a formal closing. Adding a scanned photo of your handwritten signature to the closing of the email is also a nice touch.
In the body of the letter, make sure that your topic sentences are clear and straightforward, speaking directly to different aspects of what the funder is looking for per their call for proposals or job listing. If you are applying for any kind of academic award, postdoc, or job while in the process of working on your dissertation, you must devote a paragraph (and a paragraph alone) to describing the dissertation and your progress on it.