This week's book giveaway is in the OO, Patterns, UML and Refactoring forum. We're giving away four copies of Refactoring for Software Design Smells: Managing Technical Debt and have Girish Suryanarayana, Ganesh Samarthyam & Tushar Sharma on-line! See this thread for details.
With an introductory book like Android in Action (there are others, but that's the one I'm familiar with), and by following the Android Developers Blog. If you get stuck on any particular point, googling will generally turn up introductory articles and blogs on just about any particular subject.
I would say that our book is a good one to have around. The initial chapter and the appendices try to capture most of the same basic information from the developer site about Android architecture and things you need to keep in mind when designing your application. Another great series of books that I would consider to be one of the best for Android development is the Busy Coder's Guide series written by Mark Murphy (http://commonsware.com/). Books like ours and his I believe are the most useful format because they will get you up and running, but they are also useful references to keep around even after you've gotten your feet wet.