To setup Google DNS with Google Compute Engine, this is what you would do:
Create your managed zone
gcloud dns managed-zone create --dns_name="example.com." --description="Something descriptive" "myzonename"
Get your nameservers, and update them at your domain registrar
gcloud dns records --zone="myzonename" list
Create your records and edit them
gcloud dns records --zone="myzonename" edit
Under Additions, add the A records that point to your Compute Engine VM's IP address
{
"additions": [
{
"kind": "dns#resourceRecordSet",
"name": "example.com.",
"rrdatas": [
"192.168.2.20"
],
"ttl": 86400,
"type": "A"
},
{
"kind": "dns#resourceRecordSet",
"name": "www.example.com.",
"rrdatas": [
"192.168.2.20"
],
"ttl": 86400,
"type": "A"
}
],
"deletions": [
{
"kind": "dns#resourceRecordSet",
"name": "example.com.",
"rrdatas": [
"ns-cloud1.googledomains.com. dns-admin.google.com. 2 21600 3600 1209600 300"
],
"ttl": 21600,
"type": "SOA"
}
]
}
Save and exit. You should be good to go now.