For now, before we get a full-fledged National Short Story Month off the ground with nationwide events and community-wide involvement (schools, bookstores, libraries, etc.), the best way to celebrate is, of course, to read some short fiction. If you want recommendations for collections published in the past five years (2004-08), you can visit The Story Prize site, where you can find the titles of our 15 past finalists and 61 other notable short story volumes (a feature we didn't add until 2005). The buying links may not work for all of the books, but you can easily find them on IndieBound.org and other online booksellers, if not your local bookstore or library.
And don't forget to read literary magazines that publish short stories (in print and online). There are hundreds to choose from, and you might discover a great new short story writer in any one of them, including The New Yorker.