Short Answer/opinion
I don't recommend using Mockito for Android unit testing. The Android environment feels too complex to mock. The basic approach for Android unit tests is to run them within the emulator. Thus many of the container classes are already present and need not be mocked.
Long Answer
I also am relatively new to the world of Android unit testing. I have long written server-side unit tests and found Mockito to be one of the best tools around to simplify unit testing. Mockito is very helpful in mocking the behavior of complex objects. This helps to break any dependencies that your code-under-test may have on containers (e.g. servlet container or OSGI container), or on other complex collaborators (e.g. database connection classes).
This sort of mocking works well when your containers/collaborators have well-defined interfaces.
A couple months back, I decided to try Mockito with Android development. I found that Mockito does work if you have at least 1.9.5 and dexmaker. Dexmaker handles runtime byte-code generation for Android's Dalvik VM.
The first thing I tried in my very first test was to mock android.content.Context, and I found that is was HARD. First I tried to mock only the methods that I called directly, but then I found that these called into other methods which had dependencies on application resources, ... Eventually the mocking got so complicated that it defeated the purpose of using Mockito in the first place.
So I gave in and started using the Android unit test helper classes (AndroidTestCase, ActivityUnitTestCase, ...). I was discouraged that I now had to rely on the emulator which meant SLOW test execution. Perhaps Mockito still has a place in this type of test. It might be useful for mocking things like external data sources.
Anyways, this is just my 2 cents.