{{Babel}} is for showing the languages that you know, as well as the operating system, keyboard layout, web browser, desktop environment, and text editor that you are most comfortable with. Details of how to use it for its original purpose—showing the languages that you know—are at Wikipedia:Babel.
Example: {{Babel|align=left|header=Userboxes|color=yellow|head|en|tl-1|ru-2|line|pas|:UBX/1337|!|head{{!}}Other|1RR|help desk|-|line|happy|wikipedia/WikiFairy}} produces:
The page you are now reading is the actual Babel template. If you click "edit this page", you will see invocation of Lua Module:Babel that makes the Babel boxes work. What you're now reading is just documentation for that code, transcluded inside "<noinclude>" tags so it doesn't interfere with the computer code.
In order to have Babel boxes on another Wikimedia project, you need both template and the module. Click "view source" and copy all the contents, including the computer code. Create a page called "Template:Babel" on the other Wikimedia project and put the content into it. Do the same for the module.
You also need to copy over a bunch of files with names like "Template:User en", "Template:User en-1", "Template:User fr", etc. etc. Once you've done that, users can put e.g. "{{Babel|en-1|fr}}" on their user page and the Babel boxes will be displayed.