The basic technique for mocking is to introduce an interface (if the current design doesn't have one) that provides methods for the real service (the dependency) that is being mocked. The test is testing that the class under test interacts correctly with the dependency. Correctly here means that it does what you expect it to do. That does not mean it does the right thing, as the right thing can only be determined by an integration test that uses the real components (what you envision doing by creating a real file).
So you need to have a method on the class under test that lets you pass in an implementation of this interface. The most obvious is via the constructor. You have the production constructor which initializes the class with the real implementation of the interface that hits the real file system, and then under test you pass in the mock to the constructor.
In the test you run the methods on the class and assert that the interface was called in the way you expect.
I will note that coming along after a class is creating and unit testing via mocks is of limited value, but it will help lock down behavior so that future changes to the class won't break expectations in surprising ways.
I hope that helps get you started.
Some mocking frameworks support mocking actual concrete classes, which can make a lot of sense in test-after unit tests (by intercepting calls to real classes not just interfaces). I couldn't find if EasyMock lets you do that, but JDave is probably the place to go if you need that kind of functionality. It even lets you mock final classes.