Great short stories have just one major idea at their core. This idea can come from anywhere: the lyrics to a song, an item of news, a memory or a dream. This idea, or theme, will form the backbone of your story. All characters involved should, at least in part, represent a part of this theme. It is best not to limit yourself to writing in a particular genre, as successful fiction transcends these limits.
Try to write about one or two characters. Too many characters will clutter the story. Think about the characters as if you know them - what do they like? What are they aiming for? The more you think about the characters, the more believable they will be. If the characters represent something else, as in a fable, flesh them out as much as you can. Caricatures and stereotypes may put readers off.
A good short story is defined by the way it is written. Thanks to writers such as Raymond Carver and Bret Easton Ellis, the contemporary reader will be impressed by both style and content. Be precise and economical. Also, be brutal with your rewrites, slashing any word that doesn't add to the story. In the words of George Orwell: "If it's possible to cut a word out, always cut it out."
To write successful short stories, you need to put the hours in. Any writer worth their salt is dedicated to the craft of writing. For example, Oscar Wilde would spend a day deliberating over a period or comma. The trick is to enjoy it. If a part of your story bores you, scrap it and try something else. If you are stuck for a lack of ideas, use the time refining what you have already written.