I published my story for approval and wasn't sure how to check if it has been denied or approved as I am somewhat new to publishing (been lurking for a while though).
Yeh, as far as I've heard, you'll get a message explaining the reason and how you can fix it. It generally takes about a day or two to get your story approved, so if it's not been that long yet, then don't worry! If it has been, then there's a thread here to ask Friedman (the admin) to take a look in case something's gone wrong, but generally he's very good about getting to it quickly on his own. If it was a chapter to someone else's story, then it's a bit different, because you have to wait for them to approve it instead of site staff. If the person's account is inactive, you can ask Friedman for help in the same thread. Also, this is just when first publishing a story! So once you're approved, every other chapter you add after that will be public the second you hit publish. Hope this helped!
Usually you have to wait at least 24 hours before your story gets approved or rejected. You will get not messages utill then, and you will get none either if it's simply approved, wich is most of the time. You get a message only if it gets rejected.
Not to be a smartass, but you do get a notification if your story gets approved, as I got a notif one day when my new story was... approved. The same is true for chapters, and the same is true for rejections, while also having a personal message at the top of the introduction.