Android

Launch Chrome for Android and open the website or web page you want to pin to your home screen. Tap the menu button and tap Add to homescreen. You'll be able to enter a name for the shortcut and then Chrome will add it to your home screen. add to home screen - android
The icon will appear on your home screen like any other app shortcut or widget, so you can drag it around and put it wherever you like.

iPhone, iPad, & iPod Touch

Launch the Safari browser on Apple's iOS and navigate to the website or web page you want to add to your home screen. Tap the Share button on the browser's toolbar - that's the rectangle with an arrow pointing upward. It's on the bar at the top of the screen on an iPad, and on the bar at the bottom of the screen on an iPhone or iPod Touch. Tap the Add to Home Screen icon in the Share menu. add to home screen - iphone
You'll be prompted to name the shortcut before tapping the Add button. The shortcut can be dragged around and placed anywhere, including in app folders - just like a normal app icon.