Google has been an ICANN registrar for a while, but they have never before sold domains.
Google is getting into a new business: domain registrations. The newly launched Google Domains will be allowing customers to buy and transfer domains. The cost is quite fair, just $12 a year. That offers the domain (plus up to 100 subdomains), up to 100 email addresses, and privacy protection. GoDaddy is about the same price, but they charge a few bucks more ($5 to $8) for email and privacy.
If you are dying to get a Google domain, you can try to get an invitation to their beta. Based on the beta, it isn't yet clear all the global top level domains (gTLD) they will support, but it should at least include .com, .net and .edu. I am personally pushing for .wine and .vin as well.
Google has been an ICANN registrar for a while, but they have never before sold domains. It will also be interesting to see if Google attempts to create their own gTLD. .Goog, anyone?