I would like to add buttons to a vertical menu. Is this possible and if yes, how can i best manage this with css?

What version of atahualpa?
Are you talking about in the sidebar? If so what plugin/widget are you using?

I use 3.6.7 and the standard WP menu.

so are you looking to put a button image or an actually button in the menu? In case one, you need to look at the html the WP-menu builds and determine what the CSS ID/classes are for it and then build a CSS Selector and rule for it (use FireBug in Firefox or look at the source of the page)
in case 2, you will have to edit the plugin to add the <img...> statement to the elements

I found a plugin jQuery-vertical-accordion-menu. That solves my problem.
Thanks.