Getting a book (legally) requires you have a place/app and/or website where you can buy and download one. You can run the Kindle app and with that you would log into your Amazon account and then you can get a book. You can search for a book from within the Kindle app or you can use Amazon's Market and instead of going for an app, search for a book there.
When you download a book to Kindle it puts it in it's own directory. Those are .mobi files - although I believe the app will read other book formats.
Anyway, the way Amazon kindle works is after the book is downloaded it will show up in your library in the app.
You can also use apps like Aldiko, and I'm sure others, and they all will link to a Android market or other commercial transaction process where you buy the book and then download it.
There is also the free books from Google's massive site. I think it used to be called gutenberg, but I've forgotten exactly what they call it. But there are 10s of thousands of free books available - although these are all old books.
To summarize, to get books and read them on a Ziio.
Go to Amazon market or Android Market and download the Kindle app.
Once installed, load it up and do a search for a book from within the app.
Download and buy the book and you are in business.
The above is for the Kindle app, but it's basically the same process for all other commercial book readers and sites.
I would not fool with the Ziio market, but if that's all you have then you need to get Amazon market at a minimum. The following link will get you the amazon market install file if you download it with the tablets browser. Then find it with file manager on your tablet and click it and it will install: Download Amazon Appstore application for Android (watch hands on video)