New tutorial available
It appears that the original tutorial by Brian is now 404, so here is a link to the Google one in case people see this answer first.
https://developers.google.com/places/android-api/current-place-tutorial
When this article was first written this tutorial didn’t exist.
Original:
You could try this tutorial (now 404): http://blog.brianbuikema.com/2010/08/android-development-part-1-using-googles-places-api-to-develop-compelling-location-based-mobile-applications/