Depending on the Android version installed on the device, there will be slight differences on how to complete this action.

The generic way is shown below:
1. Go to "Settings".
2. Select "Apps"
3. You will see all applications that you have on your device. Find Dragon City and click it.
4. Tap on "Clear cache" button.
DO NOT select "Clear data". Keep in mind that once you delete the data unfortunately you cannot set back the progress of your game.