Right now, we're midstream in a code rewrite, so what we recommend is that you add the story you want to follow to the Currently Reading or Recommended Reading sections of your archive profile. You can also check the author's profile and see if they do a mailing list notification, which some of our authors do. I'm not a coder, so I can't say for sure what form it will take, but I do believe we'll have a way for readers to get updates when the rewrite is completed.
As far as telling if a story is complete, that will depend on the author. Most will post an epilogue, or add an author's note at the end of the final chapter to let readers know it's finished. We do have a "Complete" tag, but it's not mandatory that authors use that tag. Some do, and others don't want to go back in and edit the story details to add that tag.