There are a number of ways to develop Android apps. The easiest way to get started quickly is to use the ADT Bundle developed by Google. The ADT Bundle provides a number of tools that are essential to building android apps.
To start go to https://developer.android.com/sdk/index.html. Once on this page click on the button "Download the SDK ADT Bundle". Once this button is clicked check the box agreeing to the terms and conditions and select either 32-bit or 64-bit, depending on your computer. After you have agreed and selected your system type click on the "Download the SDK ADT Bundle" button and the download will start. The download is a fairly large .zip file (460 mb) so it may take ahwile. After it has completed downloading you can move on to learn how to install it!