The advice and examples in So What Are You Going to Do with That?, Life After Grad School, and Outside the Ivory Tower are much more thorough than what we can go into here, but there are a few guiding principles you’ll need to keep in mind when preparing your cover letters.
Present yourself as a professional, not a graduate student. This means not leading with your academic status and selecting details of your professional experience, broadly conceived, instead of a rundown of your teaching and research (unless it’s very clear that these are relevant for the job).
Anticipate stereotypes of academics and disarm them. These include assumptions that academics are really only interested in academic jobs and consider non-academic jobs as fallback plans until they find a tenure-track job, that academics can only work in solitary conditions and are bad at collaboration, that academics can’t write well except to other academics.
Establish common ground with the person you’ve addressed your letter to. Convince them that you are really interested in this job; for example, you can use any geographic connections you might have to that area as evidence that you’re committed to setting down roots there.
A well-written letter goes a long way. Avoid sounding generic or presumptuous, and make sure that your writing is not sloppy or unclear. To increase the chances that it will be clear to the potential employer, have several non-academics give you feedback on it.
Explore the LACS cover letter writing guides and templates.