@Switch Blayde
I have an account there. Michael J. Sullivan, the successful Fantasy author I know on wattpad (although he hasn't been there in ages) said it's a must for an author to be on Goodreads.
I don't know how to use it as an author. I use it for published novels I read and review there.
Basically, before Amazon bought it and turned it into yet another way to sell Amazon books, it was mainly a site where authors could list their books and everyone could comment on and recommend books they loved (or hated, but that's almost unknown there).
Reluctant Sir, I'd write them, reporting a copyright infringement, listing where and when YOU posted the story, as well as listing the sexual nature of the story. They're pretty good about respecting copyright claims, though just like Amazon, it'll generally take them a couple of weeks to take anything down, no matter how well documented it is.
The other approach, is to try to connect to the supposed author, if they have an account there. But chances are, since the site is not a distribution site, the option to download the book is merely a link to the actual site illegally offering the story. In that case, you'd want to file an official Take-Down notice with that site.