The recent versions of Joomla provide built-in multi-lingual capabalities.
However, setting up a multi-language, requires a few more steps than just enabling the plugin and the language switcher module.
Briefly the steps are as below:
- Install the Language Packs, from the Extension Manager -> Install Languages. - This will translate system labels like
read more etc.
- Define Content Languages - These are the languages that will be assigned to the content elements (articles, menus, modules etc).
- Enable & Configure System - Language Filter plugin.
- Create the languages category structure.
- You need to create a root category for each language, e.g English, French and assign the content language you created earlier on each one. Then you can create the subcategories for each language. And remember to create a category Languages All, for content that will be used for all the languages.
- Create your main Articles and assign them to the languages.
- Create the menus and the menu items for each language. One menu for each language.
- You will need to have also an All (languages) Homepage menu item and a home menu item for each language and do all the menu items associations.
- Follow the same approach for any modules. Create the corresponding modules for each language.
- Publish the Language Switcher Module.
A more detailed tutorial can be found here
Also, you may want to consider some 3rd party extensions that provide extra flexibility or a different approach.
Update for your specific issue with the Languages Module:
Make sure you have created the Home menu items and their language associations for each language. Try to follow the steps as described in the tutorials.