Testing servlets in Java can be done in several ways. Here are some common approaches for testing servlets:

1. Unit testing with mock objects: One approach is to write unit tests for your servlets using mock objects. You can use mocking frameworks like Mockito or EasyMock to create mock objects that simulate the behavior of other objects in your system. This allows you to test the servlet's behavior in isolation from other parts of the system. For example, you can test if the servlet correctly processes HTTP requests and generates the correct HTTP responses without actually sending HTTP requests.

2. Integration testing with a testing framework: Another approach is to use a testing framework like JUnit to write integration tests that test the behavior of your servlets in a real web container. You can use a testing framework to simulate HTTP requests and responses and verify that your servlets are behaving correctly. This approach is more complex than using mock objects, but it provides a more realistic testing environment and can help catch issues that may not be visible in unit tests.

3. Web testing with a browser automation tool: You can use browser automation tools like Selenium or WebDriver to test the behavior of your servlets in a real web browser. This approach allows you to test your servlets in a realistic environment, and can help you catch issues related to the user interface and client-side code. However, this approach is more complex than the previous two and requires more setup and maintenance.

4. Testing with specialized libraries: There are also libraries and frameworks that are specifically designed for testing servlets, such as HttpUnit or JWebUnit. These libraries provide specialized tools and APIs for testing servlets and can be a good option if you need to perform complex testing scenarios.

Overall, the approach you choose depends on the complexity of your application and the testing goals you want to achieve. Using a combination of the above approaches can provide the best coverage and ensure that your servlets behave correctly in all scenarios.