How to map a fresh domain to user's blog

One of my prosite user get a new domain and tried to add it to his existing network blog through domain mapping plugin but failed and get 'invalid' message.

How to configure his DNS setting on his domain provider's configuration pannel?

I have dedicated VPS on digitalocean and change my DNS setting with this instruction. (Vanity)

https://www.digitalocean.com/community/articles/how-to-create-vanity-or-branded-nameservers-with-digitalocean-cloud-servers

1. How to configure his/her DNS setting for proper domain mapping.

Thank you for your support.