Unit testing with JUnit can be done using JUnit 3.x or 4.x frameworks. Key aspects include writing test cases as Java classes that extend TestCase and contain test methods starting with "test", using assertion methods like assertTrue and assertEquals to validate outcomes, and running tests from Eclipse. JUnit 4.x introduced annotations like @Before, @Test, and @After to respectively set up objects before each test, identify test methods, and tear down objects after tests.