Occasionally a friend or family member will be talking with someone who wants to publish their writing and the friend or family member suggests they ask me for advice. I’ve just sent off an email to one such person, and I think other people might also benefit from the advice (modified a bit to be more general). Now, bear in mind, this is about magazine publishing, and while I’ve had quite a few articles published, I’m not a magazine assigning editor and haven’t ever been one, so some of this advice is second-hand and will benefit from further insight from people who have to field queries, pitches, and submissions regularly. But it’s a start.
The thing I would suggest doing first, when it’s possible, is seeing what magazines your favourite bookstores and newsstands carry in the subject area you have in mind. Then have a look at those magazines and see which ones are publishing pieces of about the length and kind of topic you’re interested in writing. (No matter how interesting a piece is, if a magazine doesn’t have a way to fit it into their lineup of content, they won’t be able to use it.)
If a magazine looks like it publishes articles of the sort you’re writing, look at its website; there will usually be information on how to submit, or they may want to you to email first just describing yourself and the article and asking if they’d be interested in seeing it. (If they say they don’t accept unsolicited submissions, don’t bother them. They won’t make a special exception for you.) They always want to know what you’ve already published and where. If you have a blog, you can direct them to that and they’ll be able to see what kinds of things you’ve written; also, if you have some idea of how many people read your blog, and the number is large enough, you can mention it to them. Magazines tend to favour authors who bring readers with them!
Above all, when emailing editors, be friendly and polite, but also concise and to the point—the easier it is to answer an email, the sooner they will probably answer it. So just lead off with a short statement about the article (“Would [magazine] be interested in an article about [X]?”), then describe yourself and your blog and anything relevant you’ve had published elsewhere, and give a bit more detail on the article and why it would be well suited to their magazine (it never hurts to say nice things about the magazine too!), and thank them for their time and say you look forward to hearing from them.
If you feel that your article needs editing before submitting, one thing to bear in mind is that you may have friends who will happily give you advice and tell you things you need to do to it and so on, but unless they have reasonable experience in publishing, their advice may not actually be good advice. Above all, don’t worry too much about tiny points of grammar—although those are the things friends often like to pick on first, the truth is that they’re the easiest things for the magazine to fix, and if you focus too much on them it can often be to the detriment of the larger items such as good structure and storytelling. (Also, many of the “grammatical errors” that many people pick on aren’t errors, and many of their “corrections” make everything worse!) On the other hand, if you pay a professional editor to edit if for you before submitting, you may get good results, but it may cost you more than the magazine will pay you. Some magazines, though, if they see you have a good story that just needs a little structural work, may work with you on it. It really depends on the publication and editor.
Good luck!