We've done several tests installing books from Dropbox to make sure it works. The easiest way is to login to your Dropbox account from within ReadMe! and tapping on the epub-file to download and add it to your ReadMe! library.
But if you're given a link it might look something like this:
Dropbox give you the ability to link to a file directly, but also gives you the ability to link to a webpage with a download link on it. The above link is linking to a download-page, but to ReadMe! the link looks just like a direct file link.
So to install this book, simply replace the dl=0 with dl=1 at the end of the link like so: