How to activate Chrome's Data Saver feature on Android & iOS

Lurking in Chrome's Settings menu is the nifty Data Saver feature. It tells the browser to start putting all incoming traffic through compression, thereby letting you get away with less data downloaded to your device - with virtually no change from the regular browsing experience. This can shave a nice amount of data off your monthly traffic, letting you get additional megabytes (or gigabytes) to use.