DNS

If you are installing your Mail Server upon a live server that you intend to use for sending/receiving internet email then you will need to own your own domain e.g: yourdomain.com.
Your server’s hostname will need to be fully qualified to your domain e.g: mail.yourdomain.com
Additionally you should set up the following DNS records (substituting your hostname/IP where appropriate):

A record:
This will allow your servers hostname to be resolved via the internet
e.g: A: mail.yourdomain.com 123.123.123.123

MX Record:
This will tell other internet mailservers to send email for your domain to your mail server:
e.g: MX 10 mail.yourdomain.com

SPF(TXT) record:
This will tell external recipients of email sent by your mail server that your server is authorised to send mail on behalf of your domain:
"v=spf1 mx ptr ip4:10.10.10.10/32 ?all" (replace 10.10.10.10 with the external IP of your mail server)

RDNS/PTR:
This record is slightly different in that you will need to have your ISP or VPS hosting provider set this up for you as opposed to your domain name provider (unless they are the same).
This record will allow intended receiving servers to verify that the fully qualified name of your server matches the external IP is is sending email from and will reduce the likelihood of it being identified as a SPAM server.
you should request that the owner of your servers external IP create a PTR record for your servers external IP address that resolves to your servers fully qualified hostname e.g. mail.yourdomain.com