I use template
ST Ain for example.
1. Installation a new language
Login as admin, chose Extensions-> Language Manager
Click to Installation Language
Chose Language you want, for example i installation French, checking to the checkbox and click Install

Create new Content Language by click Content-> chose New

Fill all parameter in to text box.

then click Save & Close. Chose Extension-> Plugin Manager-> System - Language Filter

Then click Save & Close
2. Create a language switcher
Chose Extension-> Module Manager-> New-> Language Switcher

Module display in front-end:
3. Create Menu for language
Chose Menus-> Menu Manager-> Add New Menu, input field for language, then click Save & Close

Now, we will create menu items for each menu. Chose Menus-> Main Menu en-GB-> New

Do the same with Main Menu fr-FR

Now, in front end, we already have a module switch language, and our site was a multilingual site
4. Switch module 'About me' for example.
a. Login as admin, chose Extension-> Module Manager-> About me-> Menu Assignment

b. Login as admin, chose Extension-> Module Manager-> New-> Custom HTML, input field same as module About me, but language is France

Menu Assignment :

And our result: