Here are a few tips for submitting short stories:
Be strategic. Start at the TOP (Tier 1) and work your way down. Don't get impatient and try for more immediate gratification with lower-tier magazines right away. Getting published at a top magazine is not just good-feeling, it's career-building. You can always settle for less later.
Submit to one entire tier at a time, although if you're relatively new to publishing, you might want to combine tiers, and submit to the first 4 tiers at once.
Plan your submissions based on reading periods, and give some time between tiers. Wouldn't it be a bummer if Nothing Special Quarterly accepted your piece two hours before The New Yorker emailed you with an acceptance? If you space your submissions across tiers, you have less chance of this tragedy happening. I usually give about 2-8 weeks between tiers.
How much do scores matter? A little. For example, a magazine with a score of 130 is better-regarded than a magazine with a score of 13. But is there a quality difference between a magazine scoring 3 and one scoring 2? If there is, it has nothing to do with the scoring.
Instead, consider how your story will be treated. Will it be one of many short stories, as in StoryQuarterly, or will it stand all by its badass self, as in One Story? Are they likely to nominate you for a Pushcart, or are such honors more likely to go to Alice Munro, Lauren Groff, etc.? Does the magazine have a loyal following, or is it more random? Is it new or old?
For mail-in submissions, stock up on supplies so you can be more efficient. I have postage in different denominations, lots of envelopes of all sizes, and (can you feel the love?) a postage meter. That postage meter has saved me so many hours of waiting on line. They're not very expensive, and they're worth it.
Make a game out of the rejections. I set myself a rejection goal each year, usually 45, although it should be more. I also try to have at least 15 submissions in play at any given time. It's a numbers game—the more rejections you get, the more acceptances you get, period.
Remember that rejections are more than rejections. Editors are reading your work, and you may be making friends without realizing it. You'll get a form letter 5 times, but maybe an editor has been secretly enjoying your work, fighting for it, getting shot down, etc. Putting your work out there is the best exposure.
If the online submission fee is a couple of dollars, pay it! Magazines often use this money to pay their writers, and the fee is usually equivalent to postage and paper supplies. But if they're charging more than a few dollars...I don't know. Seems wrong to me, but make your own decision.
Always follow the magazine's writer's guidelines, even if the guidelines are stupid. You can find those on their websites.
Don't feel disadvantaged if you don't have an agent and you submit your stories the ordinary way (through the “slush pile"). I do have an agent, and I still submit via slush, mostly because I don't want to bug my agent with every story I write. Most magazines read their slush piles. That's why they have them!
If you want to drive yourself insane, see this Rejection Wiki to interpret your rejection letters.
You can also use the Submission Grinder to anticipate when you'll hear back from a given magazine (when you search at this site, keep in mind that all magazines that begin with “The"—The Paris Review, The Iowa Review—are alphabetized under T).
Keep careful records of where and when you sent each submission, when you heard back, and any editor's names you pick up from your rejections. Cultivate those relationships! If they ask for more, send them more.
Make sure your work is ready-ready-ready before sending it. Here's the most surefire way to get published: WRITE SOMETHING AMAZING.
Good luck, and never give up!