Android (Samsung, at least) instructions:
Download to your device (touch the picture you want until the menu appears and select “Download image”). Wait until the picture is indeed downloaded (it might take a few minutes).
Go to your Gallery, select the picture, tap the 3 dots at the top of the picture and select “Set as wallpaper.” It will give you the option to set as your Home Screen, Lock Screen, or both. Choose whichever option you want.