In order to install this application you need to have Internet connection (WiFi or local provider) enabled on your Android device. You can try to open the Google Play application and connect to the server using your Google mail account, tap on the upper right corner on the magnifying glass symbol, search for Khmer Keyboard and tap Install.
Also, you can visit the following official web page, press Install (if not signed in you can do that using your Google account) and the next time you connect your Android device to the Internet, the application will be automatically downloaded and installed.