Marko Gargenta has recently send around a couple of blog posts from Serete Itebete about how to build your own Twitter Application for Android.
And here are the blog posts to build your own Android Twitter client
The source code is included in the posts. Frank Maker has improved it further and posted his version on GitHub: http://github.com/fmaker/Tweety. You import it via EGit or Git via the following address git://github.com/fmaker/Tweety
You find other examples from the same website in Android Examples.