Google is working on delivering always-on, always-listening Google Assistant capability for all Chromebooks someday soon. The option to turn on the feature exists in Canary and Developer builds right now.
If you are running on one of these builds, see: Tip: Enabling Google Assistant on any ChromeOS Device
For now, though…those that are running their devices on the Stable Channel can still enable this capability if just a bit limited. The only thing you don’t gain is the always-listening capability.
To do so, for those devices that support installing Android apps from the Google Play Store install the Google app on the ChromeOS device.
You can get it here: Google
When the Google app installs, it also includes a separate Voice Search app.
To gain quick access to the Voice Search app, right-click to pin it to the ChromeOS shelf.
Now, you simply need to click or tap the Voice Search icon to kick-off a Google Assistant session. You can use it to search, ask for weather, or any other Google Assistant-capable function.