Clicking on an image will load a larger, full-sized version. After that version has loaded, right-clicking it and selecting “save image as…” will download the wallpaper to your computer.
Using a mobile browser (Chrome, Safari, etc.), tapping an image will load a larger, full-sized version. After that version has loaded, tapping and holding it will allow you to save the wallpaper to your phone. (Note: If your photos are arranged chronologically, the image may be stored under the date on which it was created and not the date on which you downloaded it.)