Google home requires you to use my openHAB or self host the my openHAB service.
There are threads with deep details about both on community.
In short though you need to add the myopenhab add on to your openHAB instance. After doing this you will configure a server to connect with. This server can be the option provided by the openHAB foundation or an instance you host yourself.
After doing this you add the openHAB skill to your google and make the connection over oauth.