Proofread your story and have at least one other person proofread it as well, ideally someone that writes at least as well as you do. Look for things like grammar, spelling, punctuation, etc. It is usually obvious when we are the first ones to proofread a story and it smacks of amateurism.
The editors of Mount Zion Speculative Fiction Review are great admirers of Strunk and White's Elements of Style. Our favorite rule is #17, "Omit needless words." The point of Rule #17 is not to cut the story down to bare bones, but to use precise language. If someone has to read a sentence twice to figure it out, you need to rewrite it.
Not every Appalachian is a hillbilly. Not all hillbillies are stupid and lazy. Even if your story is about stupid and lazy hillbillies they deserve to be written as fully realized characters and not offensive caricatures.
Exercise extreme caution when writing dialect. It is often very distracting to read phonetically spelled dialog. Use it sparingly or not at all. Instead use colloquialisms and descriptions of a character's accent. For example:
"Cumeer 'n see whut weuns dun got at th' stur."
--Versus--
"Come here and see what we done got at the store," he said with a pronounced accent.PG-13