How to install zimbra in Centos7

[phoenix]

I am trying to find a complete guide/step-by-step instruction on how to install Zimbra in Centos 7. Thanks!

Have you read the documentation and the Release Notes, there are details in both of those as well as a ton of information in these forums and all over the internet.

[phoenix]

To run a mail server (zimbra) in my local area network, do I need to get a public DNS service?

If you're going to be sending and receiving mail to other mail servers on the internet then yes, you do.