To get started with WebDriver's Java bindings in Eclipse, you'll need to install Eclipse, add a test framework such as JUnit, and a browser driver like ChromeDriver. You'll also need to set up Maven, a dependency manager, to manage your dependencies. Once you have all the necessary components, you can create a new project in Eclipse, add the WebDriver dependencies, and start writing tests. The process involves creating a test case, adding JUnit to your build path, and writing a test that interacts with the browser driver to execute a simple test. With this setup, you can run your tests using the "Run As" feature in Eclipse and see the results of your automated testing.