Providing you have met these requirements to link your phone to Google, simply type "send directions to my phone" or "send a note to my phone" into the search bar, and it will bring up a Google Now-style card for you to type in. Enter some info, hit send, and the notification will appear on your smartphone instantly (provided it's connected to the internet).
You can also set an alarm, send reminders or use the "find my phone" feature Google recently implemented using the new functionality.
This is the latest in a string of improvements to Android/Chrome to unify the experience between them. Google has struggled to create an effective note-saving feature into its Android OS, somewhat surprisingly given its high user-demand, though Google Keep has made some progress in this area in recent times, and has just been updated to integrate more effectively with Android Wear.