I don't have a widget enabled theme, I just have a general idea of how they work, so I can't give you any specifics.
Look where you downloaded your theme, it should state whether it is widget enabled or not. If you go to your dashboard, there is a message right near the top that tells you how many widgets you are using. (I'm using 0.) If I click on that, it brings me to a page that tells me that I don't have a widget aware theme. I imagine that if you go to that screen it will be relatively straight forward for adding or editing widgets from there. Alternatively, you can click on Design and then on Widgets.
A text widget is just a type. It will just put whatever text you type into the widget into the theme, so if you put your ad code then it effectively places your ad code onto the sidebar (assuming you add the widget to a sidebar widget.)
For more information, you can check the Wordpress Codex:
Plugins/WordPress Widgets « WordPress Codex