iPod Touch?
Apple:
You can get audiobooks from the iTunes Store. If he is on iOS 8 or earlier, you purchase them in the iTunes Store and listen to them in the Music app. If he is on iOS 9, then you go to the iBooks app and use the Favorites tab (to get to the Store). Your audiobooks are stored in an Audiobooks collection (similar to how PDF files are stored).
Neither is very good at surfacing audiobooks. You pretty much have to do a search, and then narrow it down to audiobooks. In iBooks there is a tab at the top that filters your results for audiobooks. I don't remember how it worked in iOS 8 and earlier.
Audible.com:
Probably the easiest, and most popular method of getting audiobooks on iOS devices is to get the Audible.com app and use their store and service. The collection is bigger (so I hear) and since the app is specialized for audiobooks, there's no confusion about the content type. Audible often has special deals for first time users that will get them one or two free books with a new account; so it's worth looking around.
Note: I don't use Audible.com myself, mostly because I'm not a big audiobook fan. Since I have, and want, very few of them, it's easier to have them tucked into a corner of my iBooks collection.
Amazon:
I'm pretty sure you can get audiobooks for the Kindle app as well, but have never explored this option.
(I am now officially tired of typing the word audiobook. We need a shorter name for this, now common, format)