To point your domain name to your VPS, you simply need to create an A record pointing your VPS IP on your DNS provider.
An A record is a kind of DNS record which links a hostname to an IPv4 address. So instead of an IP address, you can use a domain name to connect to your web server (Apache, Nginx, Litespeed, etc) of your VPS.
Most of the domain registrars provide free DNS service for your domain.
You can either use your domain registrar's DNS service or you can use 3rd party DNS services such as Amazon Route53, Cloudflare or dns.he.net
Lastly, you may utilize our own DNS hosting service.
1. If you'd like to use your domain registrar, please check the following articles:
For Godaddy
http://support.godaddy.com/help/article/680/managing-dns-for-your-domain-names
For Namecheap:
For Hostgator
http://support.name.com/entries/21479548-How-do-I-create-A-records-to-point-to-the-IP-of-my-web-host-
For Network Solutions
http://www.networksolutions.com/support/accessing-dns-manager-advanced-tools/
For others, you can simply do a Google search like: "How to manage DNS <your domain registrar name>"
2. Use Route53, Cloudflare, etc.
Simply go to their support pages to learn about how to create/edit A records.
You'd need to use their provided nameservers on your domain to use their services.
3. Alternatively, you can use your own DNS servers.
The simpliest method for this is installing a control panel such as cPanel, Direct Admin or Plesk and take a look at their support pages.
4. Using VPSDime's DNS Service
Since early October 2021, VPSDime has started offering free DNS hosting service. To use it, please login to your client area and go to DNS Management page at the top menu.