Read the magazineWith the ease of internet submissions, famous literary magazines are getting swamped by stories. The frustrating thing for editors is that while it enables them to see more good work, it often means a flood of work that clearly doesn't fit the ton or needs of the magazine. So before you indiscriminately do a mass-submission to all the big names, make sure your story actually fits the needs of the magazine. Does it seem to cohere with past stories? Does the subject matter and writing style match the magazine's? If not, you're just wasting your time and everyone else's. So be sure to do your research -- pick up a copy of the magazine and actually read it! If money is tight, many of the lit mags have selections from their journals online. Read a sample story or two at the very least before you send.
Don't bug.Editors' time is valuable, just like yours. The editors at this panel told horror stories of writers who started emailing every day for status updates a week after they had sent their story out. Understand that these magazines have an enormous backlog, and there's no quicker way to send your story to the rejection pile than to irritate someone with excessive queries. This also means not sending another story until you have heard back about the first. You can generally send the story to other mags while waiting, since the response time is so slow, but don't send to that particularly magazine again -- or pester with emailed questions -- until at least a couple of months have passed. Slow, I know, but that's the magazine biz.