To set up an Android mobile and configue it to synchronize data to and from ownCloud server, go to Play Store, search ownCloud and install the application. You will have to configure Google Wallet to pay for the download. The price is 0,79€.
Once connected you can setup an application pin to protect your data in case your Android device is stolen or lost, and allow the camera to upload the photos you take directly to the ownCloud server.
Select the configured account and begin using the app. By default, no data is passed locally to the Android device, so the files you see on your Android device are in the server. Selecting individual files gives you different options.