This post is just about providing the reader a quick start point. There is plenty of documentation and of excellent quality in the official developer site, but we are going to focus on the required tools.
In order to start developing Android you will need to install the Eclipse IDE, you will find it here.
Then you will need to Android specific downloads. For the SDK just follow step by step the download and installation instructions. Here you will select the basic tools to install, plus the target platforms. Each platform allows you to develop targeting to an specific device. It is advisable to install the latest Platform and the least you want to support, select the least supported platform is a personal decision, but looking the Android Dashboard sounds pretty safe to choose API Level 10 as the least supported platform (this would cover around 80% of android devices). It is also advisable to install the sample sources for each SDK platform you select, so that you will have some real code to take a look at.
Once you have installed Android SDK you will need to install the Eclipse plugin that will aid your development process. This is perfectly explained here, so we are not going to get deeper into this.
Now you are ready to develop for Android. We recommend reading and following the step by step tutorial about Creating your first project.