your local butch

I was trained in the dark arts of the cover letter by my mother, who is a hiring manager. And her training has paid off: I've been consistently told my cover letters are excellent. Let me pass on the wisdom.

The job of a cover letter is to give a prospective employer strictly more information than is on the resume. This is where you take the resume contents and put them into context. You look at the job requirements (you are looking at the job requirements before applying, right?) and look at your resume and ask the question (in your head) "why would a person think this candidate would be good for this job?" and your cover letter is the answer to that question. If you don't answer that question, the hiring manager is going to have to do it themselves, and you have way more information to work with than they do.

This is especially important if you're moving from one industry to another, because then the relevant connections aren't obvious. It's also very important if you're overqualified, because then you can use the letter to say "I know it looks like this job would be too entry-level for me, but I'm interested to pursue it for reasons x, y, and z". You can also use this space to explain away something that might otherwise be disqualifying, like job-hopping or a long break in employment. The tone to strike here is always matter-of-fact and constrained to topic - don't go into detail about health stuff or personal tragedy, just tell them what they need to hear: that this period of your resume was affected by [bad thing] but that it's now in the past and you're looking forward to the next chapter. Remember, one of the things they're trying to learn is whether you'd be content in this role, or whether you'd be miserable and leave after 2 months, which would force them to do all the work of hiring again. You're trying to establish that you will fit right in and not cause problems. Knowing what drew you to this job in particular (and don't just say 'money', that's true for everyone) helps with that.

If you don't know how to write a cover letter, here's a very basic template:

Start: letter-style salutation. If you don't know who the hiring manager is, "hiring team" or similar is fine.

Introduction paragraph: who are you, what job this is, why you are interested in it

Paragraph 1: take one part of the job description and explain how your previous experience and skills would make you good at this aspect of the position you are applying for. This should involve a brief description of what you have done previously (in a job, in education, in volunteer work, etc.), not belaboring the point, and then how those skills apply. Talk a little about how those skills have helped you in a previous position while explaining those duties. This is also where you would explain if you have transferrable skills! Say you haven't worked in this exact field before, but you have skills (so-called hard skills OR soft skills) that apply to this position. This is where you convince the hiring team that these skills apply to what you are applying for.

Paragraph 2: basically the same as Paragraph 1, but with a different part of the job description. Try for something with a different skillset.

Paragraph 3: same as above. You don't need as many as three paragraphs. You can have as few as one. It all depends on the job and how much you have to say about it.

Closing paragraph: Conclude as to why you would be a good fit for the job. Thank the hiring team for considering you and re-emphasize why you want to work there. Sum yourself up in a punchy one-sentence conclusion. Sign off like a letter.

This should all be about a page of text, as the OP mentioned. It's not rehashing your resume, but explaining those skills, elaborating on them, and convincing the person or people reading these letters that you should be interviewed because you are a good fit. (Don't say that in so many words -- "I would be a good fit because...." but rather do it professionally, like "I would bring my passion for and previously strong results in teen literacy to [teen literacy librarian role]")

It's also okay to write a few basic templates for yourself! Just be very very careful to tailor them to each position, and don't accidentally send the template itself or the exact same cover letter to multiple places (or worse, the same place multiple times). (When I was most recently job hunting I accidentally sent a cover letter with the name of a different place because I copy/pasted and didn't proofread closely enough..... don't be me LMAO)