Most Android browsers let you add a website shortcut to your home screen. The method to do this is largely similar across browsers and can generally be found in the browser's menu options.

You can now easily pin apps to the taskbar in the latest Android Canary release. This will make Android's Desktop Mode even more useful.

For phones running Stock Android, you can use the Settings widget to add shortcuts for various settings. Long-Press on Home Screen: Long-press on any empty space on your home screen.