Jenkins can, with the help of an SDK and a few plugins, be set up to automate the building, deployment, testing, and publishing of Android applications. To build Android applications, you need the Android software development kit, which you can download from:
http://developer.android.com/sdk/index.html
When it is downloaded, extract the archive to a local directory. Then edit and add the following environment variables to your system:
export ANDROID_HOME="<location of extracted files>" export PATH="$ANDROID_HOME/tools:$ANDROID_HOME/platform-tools:$PATH"
Once this is done, update the SDK and verify that your Jenkins user has read and execute permissions on the SDK executable files.
To run an Android emulator as part of your build process, add this plugin to your Jenkins server:
https://wiki.jenkins-ci.org/display/JENKINS/Android+Emulator+Plugin
Note that this will attempt to install an Android SDK for you if it doesn't find one. It's often preferable to set up the SDK...