At a high level, your widget can do whatever it needs to do (including calling a web service) inside it's implementation class. The system calls a render() method on the widget each time the page is refreshed in run-time, or whenever the widget is moved around the screen in design mode.

Inside the render method, you could call a class/method that handles the web service call and returns the appropriate data.

The render method is responsible for returning an XHTML string representing it's output/display, but how you build that string is up to you (from the web service response data in your case).