You don't need to do any further setup. If you own the second device, simply login to the Google Home app using the same account you used to setup the device. If you want to share the device with another home member, invite their account/email address to the home:
Share a home and devices in the Google Home app - Google Nest Help
Note that even if the device only appears in the Nest app, you still need to use the Google Home app to manage home members.
The email address you invite must be a personal Gmail account, or if the person you’re inviting to the home uses another email provider, they must create a Google account using that email address. Once they receive and accept the invite, your device(s) will show up in their Nest or Google Home apps, as appropriate.
