Select the Mission you would like to complete, and click the blue 'Do this Mission!" button as shown below:
You will then be taken to the in-app camera where you can choose to take the picture within the app, or upload one from your device:
If the creator set the Mission to live capture only the upload from device icon in the lower left-hand corner will not show for that Mission, and you will only have the option of taking the picture live within the Goosechase app at that time.