I am hardly an expert, having only started to submit stuff to magazines about three or four months ago, but for what it's worth, my advice would be as follows:
1. Be sure you are as familiar as possible with the type of material the magazine publishes. Obviously, there is no point in submitting a horror story to Gardener's Weekly. But, in addition, there are within-genre variations, in terms of style, target readership, etc. Don't make the mistake of thinking that because Magazine X has published somewhat simplistic, naively-written, formulaic stories it will jump at the chance to publish your complex, erudite, multi-layered opus. Magazine X publishes simplistic stories because it knows what its readership likes, and its readership likes simplistic stories. If you have written a complex story, send to Magazine Y, which likes complex stories.
2. Spread your net wide. Favour magazines which accept simultaneous submissions, and send a given story to three or four mags at once. Wait until you get responses, and hopefully feedback, from these mags, re-read and revise your story [assuming it is not accepted], and send it out to another three or four. Repeat the above.
3. Understand that it is at least partly a game of chance. Whether or not your story gets accepted depends on such things as: which editor it lands in front of; whether said editor is having a good or a bad day; what stories they have just read; what stories the magazine has just published; how much space the magazine has and how long your story is; etc. Some magazines try to put together stories which complement each other in a given issue, and therefore your story may be chosen or rejected not only for merit but also for the extent to which it fits with some of the other stories the editor wants to publish. So being rejected may not mean very much [but see below].
4. Being rejected may well mean that your story just isn't good enough. In fact, it probably does. Swallow your ego and revise the story. In every instance that I have feedback from magazine editors, I have had to sit back and kick myself, because their feedback has been spot on, and in retrospect I would have been mortified had they published the poor effort I sent to them. If you are lucky enough to get feedback, act on it to make the story better, and send it out again.
Just my 2p-worth....