Google Cloud DNS is basically an alternative to DNS services such as DigitalOcean's free DNS Manager, Amazon Route 53, DNSimple, DynDNS, etc. It doesn't have anything to do with your droplet so you will need to configure your domain (via your registrar's control panel) to point to Google's Cloud DNS nameservers in order to use it. Once you've done that, you can add DNS records that point your domain to your droplet.

@techaddict009, here is a basic guide for setting up a domain with Cloud DNS:

https://www.zeitgeist.se/2014/05/01/google-cloud-dns-step-by-step/