A DNS server is used to enable a machine to translate a website name, like www.google.com, into an IP address. This process is known as Hostname resolution. Hostname resolution is done because a machine doesn't understand names and human are more comfortable with names. Using this, a machine can communicate with one another easily.
Now, to verify that your machine is able to resolve hostnames simply ping to any website like www.google.com, when you use the ping command to a host using its name, OS will perform a resolution and obtain its IP address and display in the ping command.
This way you can verify as your DNS server is configured or not.
Here is an example to show how it works:
C:\Users\priyj_kumar>ping www.google.com
Pinging www.google.com [216.58.197.36] with 32 bytes of data:
Reply from 216.58.197.36: bytes=32 time=40ms TTL=56
Reply from 216.58.197.36: bytes=32 time=39ms TTL=56
Reply from 216.58.197.36: bytes=32 time=38ms TTL=56
Reply from 216.58.197.36: bytes=32 time=40ms TTL=56
Ping statistics for 216.58.197.36:
Packets: Sent = 4, Received = 4, Lost = 0 (0% loss),
Approximate round trip times in milli-seconds:
Minimum = 38ms, Maximum = 40ms, Average = 39m
This way you can verify your DNS Server. Hope it helps.