There are lots of threads that will guide you to various pieces of this process. It is basic enough that I don't think much of anyone has written a howto for the simple reason that it would be old news to most people who set up mail servers.
But there are a few basic steps you need to do:
- Decide if you are going to connect from outside using IMAP or POP
- Configure your firewall and network so the appropriate ports for IMAP and/or POP for receiving and SMTP for sending mail, are available from public IP addresses
- Configure your mail accounts to allow POP or IMAP as appropriate
- Configure your mail server to accept the correct type of login--SSL/TLS, cleartext (NOT RECOMMENDED)
- Set up the mail client on your home machine according to the settings you have created above.
If you are having particular trouble with, or do not understand, any of these steps, post more questions.
I would add that I'm unclear why you would have two separate mailservers as you describe (internal and external), on the same IP address. SMTP.xxx.yyy sounds like the "sending mail" portion, and mail.xxx.yyy the "receiving mail" portion, of the same server.
Please don't take this wrong--I'm not trying to talk down to you--but your questions suggest to me that you may not be familiar with the basic terminology of email servers. If this is true, you have an adventure ahead of you! You might want to start off with
this article, which gives a pretty good overview of the "nuts and bolts" of email technology. And if I'm misunderstanding and you already know this, then please accept my apologies!
Cheers,
Dan