This site now speaks several languages. Nothing was translated automatically: each language has its own content, its own categories and its own menu.
Three parts, and no more
A multilingual Joomla site rests on three parts. The first is the language filter, a plugin: it decides which language to show, and sets aside the content of the others.
The second is the menu per language. Each language has its own, with its own home page. That home page is what tells Joomla where to land when this language is picked.
The third is the language switcher, the module with the flags, top right. It has no cleverness of its own: it lists the published languages, and follows associations where there are any.
What happens when a part is missing
With no language filter, every language shows at once. With no home page for a language, the switcher falls back to the default home page, in the other language. With no association, the switcher still works, but it returns to the home page instead of the matching one.