Article snapshot taken from Wikipedia with creative commons attribution-sharealike license.
Give it a read and then ask your questions in the chat.
We can research this topic together.
Your Babel box is for saying what languages you know, as well as what operating system, keyboard layout, web browser, desktop environment, and text editor you are most comfortable with. Details of how to use it for its original purpose, saying what languages you know, are at Misplaced Pages:Babel. Details of how to use it to say what technologies you use are fairly scattered, but a large assortment are at Category:Wikipedians by technology, or in Category:Wikipedians.
Template:Babel - Allows 1 to 100 boxes. Format: {{Babel|<box1>|<box2>|<box3>...}}
Template:Babel-N - Allows any number of boxes. Format: {{Babel-N |1={{User <box1>}}{{User <box2>}}{{User <box3>}}...}}
Custom headers, footers etc.
To specify a custom header, footer, bordercolor or color add the parameters header=HEADER (default: Misplaced Pages:Babel), footer=FOOTER (default: Search user languages), bordercolor=BORDERCOLOR (default: #99B3FF), and/or color=COLOR (default: white). Call the '!' userbox to start a new column after that point or the '-' userbox to insert a blank row. You may also use '|align=left' to display the babel box on the left side of the screen rather than the default right.
How to get Babel boxes to work on other Wikipedias
The page you are now reading is the actual Babel template. If you click "edit this page", you will see a bunch of computer code that makes the Babel boxes work. What you're now reading is just comments in that code, inside "<noinclude>" tags so it doesn't interfere with the computer code.
In order to have Babel boxes on another Wikimedia project, just copy this page to that project. Click "edit this page" but do not actually change this page. Just use your computer mouse to copy all the contents, including the computer code. Create a page called "Tempate:Babel" on the other Wikimedia project and put the content into it.
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.