Based on what you have written, it sounds like the DNS is being provided by your domain name registrar in which case setting the A record to the IP address of your server is all that would be necessary.
Many times people use the DNS service provided by their hosting company in which case you must specify the name servers to use in your domain management area at your registrar. I prefer to use the DNS provided by the registrar because you can point your IP address anywhere and not have to worry so much about propagation issues involved when actually changing the DNS servers. (With the downside being that if your host ever changes the IP address you are on they cannot automatically update the DNS record like they could if they managed the DNS.)
The number of DNS servers used by your registrar is most certainly more than one. You can check the number of nameservers for your domain using the nameserver lookup tool at the link below. In the DNS Lookup box input your domain name and then select Name Server (NS) from the drop-down box and click "lookup". Then do it again for the www version of your domain name.
My DNS is with my registrar (Namecheap) and they are using 5 DNS servers.