If the widget is built correctly the styling is set via a CSS file in the widget.
You can include the new style changes in your theme. This will overwrite the styling of the widget. A good thing is to test your new styling in using the browser development tools and inspect the elements (right click). Check some tutorial how to insert styling at run time to test what works best for you.
In some cases widgets are have hard coded inline styling, that you can not overwrite with CSS.
Then you need to hack the widget (unzip, change zip and go)