I started out reading Application Fundamentals to get the 10,000 foot view of the framework. From there I bought Pro Android 2 in order to quickly learn about various Android subjects. I don't necessarily need to know about all of these subjects now, but it helps to know about other options. For instance, I don't need to use Content Providers right now, but they are a useful topic to be aware of if my app's requirements head in that direction. After flipping through that book I took a look at some of the tutorials that related to my application.
I'm currently developing my application with great success, although I continually have to reference the Documentation. Answering questions on stackoverflow has also helped me quite a bit, because I often learn more about the framework in researching for responses.
Also, make an effort to read a Technical Article every day from Developer Resources. Most of the articles are easy to follow, and they often cover issues you may not consider (such as the article on Avoiding Memory Leaks).