To understand how a good story works, you need to actually read books to see how well a story flows form page to page. You also have to concentrate on the genre you want to write about yourself, so if you want to write horror stories, don't read chick lits. And vice versa ofcourse.
If you want to concentrate on short stories, there is only one writer you need to look for and that is Anton Pavlovich Chekhov, who is considered as one of the greatest short story tellers ever. Luckily for you a lot of his stories can be read online at www.online-literature.com/anton_chekhov/. So feel free to have a look there and check out his short stories. He really knows how to draw you into the story from the first few lines you read.
For Science Fiction aspiring writers, there are a several writers you should really read their books from, and those are Isaac Asimov, Arthur C. Clarke, Jules Verne, H.G. Wells, Philip K. Dick, Ray Bradbury and Robert A. Heinlein. Those writers really formed Science Fiction as we know it today.
Aspiring Horror writers, should really read the books from the following writers, and those are: Clive Barker, Richard Matheson, H.P. Lovecraft, Edgar Allan Poe and ofcourse Stephen King.
Anyway, you get the idea that you need to look for the best writers of the genre you want to write in, and read their books.
Happy reading and writing everyone!