There are many paid and free "DNS hosting" services,
which can make this process easy.
How it works:
You point your domain name to DNS services of the "DNS hosting" service,
and then from their account you point DNS record of your domain
to IP address of your VPS.
List of some free services:
How to work with them:
1. Create free account in their system
2. Add your domain name to the system ("domain.com")
3. Add DNS Recors which you need
4. Point your domain to DNS Servers provided by the service
In 1-24 hours your domain will be activated and will work on your VPS.
Which DNS Records do you need:
1. "A record"
Enter here your domain name or subdomain name
and IP of your VPS server.
2. "CNAME" is an "alias"
You can use it to poin "www" subdomain to main domain.
So create CNAME record, as Name enter - "www", as destination -
your domain "domain.com"
3. "MX record" - used to point emails to your (or different) Mail Server.
(for example you can use Google service to receive emails based on your domain)
For additional information about these and other DNS Records please search in google.