You can add Categories to the sidebar (or any other widgetized area of WordPress) via, “Widgets.” You can get to Widgets via the WordPress dashboard and just about every page within the dashboard.
Once you’ve accessed the Widgets screen you should be able to drag and drop “Categories” into the sidebar. I’m pretty sure you will understand the screen once you see it.
If there is one thing I really like about WordPress; it’s the fact that they try to give you quality supporting text on the page so that you don’t have to constantly sit with a tutorial open to understand everything. It really is designed well; from where I sit anyway.
I usually end up running the widgets window in Accessibility Mode. However, I do know that in regular view, if you click on the Categories Widget at any point before or after dragging it; there’s an option to have it work as a dropdown menu.
It’s really not Rocket Science. So, if this blind guy hosting websites can do it, “So can you.”