First off, what version of Exchange are you planning on trying to setup? If it is a SBS, it is going to be the easiest for beginners as it steps you through the process. If you have just exchange server, in an ideal scenerio, you would install it on a second server as it is not recommended to install on a domain controller, but, if need be, it can be accomplished.
For starters, you need a domain name. If you dont have one go out and register it with say Godaddy, HostGator or one of the other million domain registers on the net. Once that is completed, you should have some sort of user panel to control DNS. (If not, the hosting company will normally make the changes for you). Once the domain is registered, go into the DNS panel and make a couple changes. First, create an A record and have it pointing back to your WAN IP address (
www.whatismyip.com). I would call it something like mail, webmail something along those lines. This is going to be the name you access OWA (outlook web access) with; ie mail.yourdoamin.com. Next you will want to change the MX record and also make it point back to your WAN IP Address.
Now on your exchange server you will also want to create a MX record and point it to the LAN IP Address of the exchange server. Also create an A record for mail, or webmail and have it poining to the LAN Address of the Exchange Server. You will also need to open port 25 on your firewall. You can test to see if the outside world can connect to the exchange box by going to
http://www.mxtoolbox.com/ and putting in your mail server information.
Here is a tutorial on setting up exchange server 2003:
http://technet.microsoft.com/en-us/library/bb124186(EXCHG.65).aspxIt is a little more complex than what I have posted, but a good start. There are plenty of tutorials on the web that will help as well.