You can set up a Messenger Customer Chat plugin by going to your Facebook page settings.
Go to your Facebook page Settings
Navigate to your Facebook page settings by going to your page and clicking on Settings in the top right navigation.
Go to Customer Chat Plugin
On the left sidebar, click on Messenger Platform and at the top of the page, click on jump to section on the right of Customer Chat Plugin.
Set it up!
Now you can click the Set Up button to start going through the wizard.
The steps are straightforward. To fully add it to your site you will need to implement the code snippet to your website.