I herewith submit my [short story/essay] XYZ" for your consideration.
Sincerely, Joe Shmoe"
If you don't want to go with that short short version, feel free to use my cover letter template. Here are a few general pointers:
- Address the editor by name if you can find out from the masthead who it is. If you're sending nonfiction, try to find out who the nonfiction editor is. I once heard an editor say that it's nice to know that you know who they are and that you've done that extra bit of work to find out and are not just mass mailing them. But if the editor's name isn't clear from the masthead, don't waste time on this. Just say "Dear Nonfiction Editor."
- Don't explain what your piece is about. It should speak for itself. This is not a query letter trying to sell a book, or pitching a magazine article.
- Give a few details about yourself. This is really the only purpose of this cover letter. The editors might like to know who you are as writer. If you have publishing credits, mention a few, your most recent, preferably. Don't give a whole list of every place you've been published. That comes across as pompous.
- Don't worry if you don't have publishing credits. Just say how long you've been writing, and what you've been writing, or what topics you're particularly interested in. Editors love discovering new talent, that's one of the highlights of running a literary magazine.