In a nuttshell, you need a pop3 mail server and the domain name forwarding to your machine (with MX entries and all).

Now, getting down with it...
The pop3/imap mail server varies OS to OS; it isn't hard to find one at all in all reality.

The hard part is the domain name, most isp's are dynamic meaning they change, so using ip pointing with the domain is near impossible.

There are a couple of programs that tie into domain registries or the various free domain pointer services for redirecting the domain to your ip whenever your ip is updated (or having a heart beat connection that sends a request every 5-10 minutes).

For sending mail you're looking at something called SMTP (or sendmail in *nix).

I'll repost with some links.
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