Android provides various packages for testing like
AndroidTestCase ApplicationTestCase InstrumentationTestCase ActivityInstrumentat
I found this tutorial from droidcon 09 to be really informative. Complete with downloadable working source code examples.
Edit: The link seems to be dead, as pointed out in comments.
It walks through creating a Celcius to Fahrenheit temperature converter test-first using ActivityInstrumentationTestCase2, TestCase and AndroidTestCase.