If the Books section isn't showing on your computer's iTunes then make sure that Books is ticked on the General tab in Edit > Preferences. Books shows as a tab on the device on the right-hand side of iTunes, not under the device name on the left ( and the tab syncs to the iBooks app not to other apps).
To get books bought from Amazon into the Kindle app you use the Kindle app (there should an Archived Items button at the bottom), and similarly Kobo books are loaded via the app (on an iPad I drag the bookshelf down and it then refreshes which any new purchases from their site).
Apple introduced rules that meant that 30% of anything that was bought from within an app had to paid to them. So Amazon and Kobo decided rather than paying that they would remove the Store buttons from within their apps - which for Kindle all it did was take you to a browser anyway, so all that has changed is that you have to go to their website yourself instead of pressing a button.
Books that you buy on other sites, if they don't have any digital rights management which would then tie them to that store's app, can be loaded onto the device via the Books tab (for iBooks), or via the file sharing section at the bottom of the device's apps tab (Kindle and Kobo show there for me)