Primarily, we will focus on unit testing using standard, robust relative integration tests which broadly test multiple pieces of the app's functionality--all at the same time. While you are considering the types of tests you would employ, you need to consider replacing the dependencies that typical apps have, such as Azure Tables, SQL Azure, etc. so the tests can specifically focus on the areas of the app likely to run the logic you are testing.
Developers use a variety of testing methodologies to test Windows Azure applications, including the unit testing of frameworks, mocking of the frameworks themselves and automated unit testing. Since there is so much involved in the testing process, we'll outline some essential Windows Azure testing techniques here.