Good job making it this far. BIND is a good choice for DNS software but it is not a trivial exercise, configuring and maintaining your own DNS infrastructure.
Before I link you to the relevant tutorial, have you considered using DigitalOcean's DNS service, located in your Cloud admin panel under "Networking > Domains"?
If not, I would recommend trying this first as it will be simpler, faster and more reliable than running your own DNS server.
Here are some relevant links to hosting your domains on DigitalOcean's DNS:
It's a two step process, add your domain then add your records (eg, "www"):
If that doesn't meet your requirements, here is a tutorial on setting up BIND for DNS - keep in mind that it expects two servers in this setup, a primary and a secondary, in case the primary goes down:
The tutorial is a little older, so be on the lookout for differences with your current operating system. The BIND info should still be valid.
Hope this helps and good luck!
Bind, the most popular DNS server, is used as the backbone of much of the world's DNS system. In this guide, we will discuss how to configure a pair of DNS servers to act as primary and secondary authoritative-only DNS servers for your domains. We will be demonstrating this on Ubuntu 14.04.