If you haven’t made any changes to your code, the plugin should automatically use the HTML as defined when the sidebar was registered (before_widget, before_title, etc). If nothing was defined, then WordPress automatically defaults to using list items and h2 headers.
I’m using a custom theme with 7 sidebar widgets already (1x header, left sidebar, right sidebar and 4x footer). I was trying to make the right sidebar the default one and have your plugin replace it depending on the page.
My own code for this right sidebar in the function.php is: