The steps are simple, you should first have a real IP connected to your exchange (or Firewall/NAT in general), and it should be fixed, meaning that it doesn’t change when you restart your server, then the next step is that you must have access to the DNS system that is responsible for your domain name “mycompany.com” in my example, you should create in it an A record that maps for example “mail.mycompany.com” to the real IP you have on your server, then you creae an MX record that maps the domain “mycompany.com” to the the A record you created earlier, that is “mail.mycompany.com”.

When any mail server (i.e. Hotmail) on the internet tries to send a mail to say user1@mycompany.com, that mail server will query the DNS hirarcy for the MX record to know who is the server responsible for your domain, which will return mail.mycompany.com, then it will try to get its IP address, this is where the A record comes in, after that it will contact your mail server (or Firewall/NAT pretending to be a mail server) and sends the mail to it. Up from here, its a configuration settings in Exchange or ISA or whatever.