The Android client is not available in the Google Play store yet but instead is provided as a direct apk download. This means that you have to modify your phones security settings in order to be able to install the application.
Once the open beta is over the TeamSpeak application will be available in the Google Play store and you can revert the setting.
Make sure your phone meets the system requirements:
You need a phone with at least an ARMv7 CPU (hardware FPU required).
Your device needs to be running at least Android 2.3.3
CPU Speed of at least 800Mhz
Wireless or at least 3G connection is advised (you may experience odd behavior due to packet loss otherwise)
Go to your system settings and then choose "Security" (Android 4.x) or "Applications" (Android 2.x) and check the "Untrusted Sources" option to allow installation of applications not received through the Google Play store.
Download the application or scan the QR code using your phone:
For those of you who already participated in the closed Beta test that has been running for the last few months, please note that the closed beta will not update to the open beta, but rather you will have to uninstall the closed beta and then install the open beta using the above link / QR Code.