Hi/Greetings,
My name is <name>. I'm currently <insert current occupation> and I'm writing <insert when you're writing>.
In the past I've done <work/study>. I've written <genre> for <x> years and I have been published <y> times. [if you haven't been published, write that instead].
When I'm not writing or working I like to <interests>.
My dream/ambition with my writing is <secret world domination plan>.
Signed.
Dear Fiction Editor,
I'm submitting my story "The Stranger" for consideration. The word count is 2500 words. I am unpublished, so I appreciate the opportunity to be considered for Fancy Magazine.
Thank you for your time.
Jane Smith
Dear Wendel Greene,
I'm submitting my story, "The Stranger," for consideration. The word count is 2500 words. I thought my story could be a good fit for Fancy Magazine after reading "Men with Small Hats" by John Doe in the October issue.
My stories have been published in Galactic Hat, Bluebeard's, and Mirror Mirror Journal. I'm a ventriloquist born and raised in Logan, Utah, and I have a BFA in balloon animal husbandry from Sad Clown University.
This is a simultaneous submission.
Thank you for your time.
Jane Smith
Don't explain the story or apologize for submitting. Be brief, specific, and courteous. That's my advice, anyway.