Adding and styling new left sticky sidebar in wordpress theme

I'm trying to add a new sticky left sidebar in my main content page to display a vertical menu (created from H2 title anchors).

Idealy I would like it to approach this awesome menu from the bootstrap site.

I've generated the sidebar using the dynamic sidebar function.

I can drag and drop widget into this sidebar, so it seems functional.

The sidebar display itself at the bottom of my content page, just before the footer.

I've add some CSS in my style.css but it doesn't seem to do the trick.

My questions :

Where should I put the function ? Into which template files ?

How to make it display properly on the left side of my main wrap ? (using CSS)

First question on StackOverflow, please be gentle. :)

Thanks for your help,