In the settings, there will be a new entry called Handwrite that you can enable. Be sure to save your settings after enabling it to make sure it works.
Go to the Google search home page and tap the new Handwrite icon in the very bottom-right of the screen and write anywhere on the screen. When you stop momentarily, your handwriting is converted to text and entered into the search bar, also activating Google Instant. You can still continue writing anywhere or you can tap a suggestion or result whenever you like.
Remember that Handwrite is still in beta and it may not work very well at the moment. Google says that it works best with straight block letters. They also say that this feature is meant to complement, rather than replace typing.
It is currently available in 27 different languages and works on Android and iOS.
I predict that Handwrite will surely get to Google's mobile apps at some point as well. Let's see how long the beta tag stays on.