Downloaded a book and don't know how to start reading?

Where did you download the book from?

There is an iTunes app on your iPad (it's only the iTunes store, for buying/downloading music, films, TV programmes), unless you've hidden it via Settings > General > Restrictions > iTunes Store 'off'. To log out of an account tap on your id at the bottom of the Featured tab in the iBooks app (you can also log out by tapping on your id at the bottom of the Featured tab in the iTunes store app, and via Settings > iTunes & App Store)

The book is on the bookshelf in the iBooks app ? You could try closing the iBooks app via the iPad's taskbar and seeing if you can read the book when you re-open the app : Force an app to close in iOS - Apple Support

If not then try deleting the book via the Select button at the top right of the bookshelf and redownload it via the Purchased tab (bottom right) of the app and see if you can read that copy on the bookshelf.

You've tried closing the iBooks app via the iPad's taskbar as per my above post ? You could also try a soft-reset : press and hold both the sleep and home buttons for about 10 to 15 seconds (ignore the red slider), after which the Apple logo should appear - you won't lose any content, it's the iPad equivalent of a reboot.

The sleep button is the button you press to turn the iPad off, and the home button is the button you press to close an app.

Do you have iBooks on your Mac to see if it opens on that?

There is another reset you can do on the iPad: Settings > General > Reset All Settings.

The next step is to do a backup and restore:

Back up and restore your iPhone, iPad, or iPod touch using iCloud or iTunes - Apple Support