I've had several people ask me for tips on how to submit to literary journals. First, remember not to be intimidated. There are currently 5,006 markets listed on Duotrope.com (a submission tracker service website). Most of these publications are in need of fresh writers. All of these publications should have started because they love writing and promoting writers. With that many markets you have a wide range of quality and styles. You can find a fit for your work. And, you should have a couple journals that your writing may not be polished enough for yet, but are striving to get in one day.
Don't waste your time doing an ungodly amount of research. All of the journals will say read them, but if you read just one copy of each one listed, you'd be dead before you ever got around to doing any submitting. That being said, DO get a feel for some of the different journals to understand better which ones match your own style. I can recommend Duotrope.com. It's about $50 a year and I have used it. It has links and summaries of all the journals both online and print, and it will keep track of your submissions (that you enter in the database). It is a time saver. If you don't want to spend the money, you can start out with a basic spreadsheet of your submissions. Poets & Writers has a detailed list of literary journals for free.
Don't waste your time submitting to the top dogs. I know they all say they are looking for fresh, aspiring writers to put alongside the famous names already in their pages, but their idea of "fresh and aspiring" really means MFA graduates that have already gotten picked up in other journals and possibly have a signed contract for their first novel. On the flip side of this advice, don't waste your time sending your writing to journals you might not be proud of holding up at your book club. Maybe you should think twice before sending your memoir about holidays with your grandma to Erotica Weekly. Get a nice comfortable middle group to start out, where all the journals you submit to are relatively on equal ground. These are the ones that are willing to take a shot on your work. They need you as much as you need them. There's only so many Lorrie Moore manuscripts to go around.
Part 2 I'll address simultaneous submissions and cover letters. Questions can be sent via my contact tab.