At long last Kobo has published the user manual for the Aura One. I found it via Mike Cane, and among other things it explains the excruciating process for borrowing an ebook (which I detailed in an earlier post, so I won't repeat it here).
Coincidentally OverDrive has also posted instructions which more or less explain the same process as detailed in the user manual.
To be honest, I don't think you should read either set of instructions, nor should you try to borrow library ebooks on the Aura One.
The official instructions tell you how to do everything from the Aura One, but really the easier way to go about borrowing ebooks is to use the OverDrive/library website first.
Edit: And just to be clear, I am suggesting that you visit the website from your PC, not your Aura One.
After being prompted by a reader (Thanks, Cynthia!), I found that it was much faster and simpler to first browse the website and borrow an ebook, and only then pick up the Aura One and tell it to sync.
That borrowed library ebook will show up on the Aura One’s home page as a “New” title which can be downloaded and read.
And when you're done reading it, you will have to go back to the website to return it, so while you're there you might as well use the site to borrow your next ebook.
This still falls short of the promised "one-touch OverDrive library lending access", but the website trick does make it significantly easier to borrow ebooks from OverDrive. It's about half as much work as the official method, only a tenth as frustrating, and much faster.
So if you bought an Aura One, it's well worth your time to familiarize yourself with the OverDrive website,