As each ZAZA.rocks bag is just a url opened in your internet browser of choice, the process to save files, whether pictures or other, implicitly depends on that browser and underlying operating system.
Here's the flow for a mobile iOS device (iPhone, iPad) with Safari, saving the picture to your Photos app. Alternatively, you can watch this how-to video.
Swipe right on a picture in your ZAZA.rocks bag, and click on Download icon.
Click on View in the appearing pop-up. The photo now appears in full resolution.
Click on the box-with-outgoing-arrow icon, and select "Save image".
The photo is now added to your Photos film roll.
Related to this topic, have you read our ZAZA.rocks story on the Designated Picture Taker?