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Do so by browsing or running a search for a specific image. In Google Web Search, tap IMAGES below the search bar to see the images associated with your search. The image will be saved to your device, and you can view it in the Photos app. On devices with 3D Touch, like iPhone 6S and 7, tap the Share icon -- the rectangle with an upward-pointing arrow below the image -- then tap Save Image. Not all Web images are downloadable.

Summary:
Open a Web browser. Find an image to download. Tap and hold an image to open it. Tap Save Image.