I found it to be a bit easier than that, but this may be a special case.
I have a cable modem which allows multiple ip addresses. The modem plugs into a hub, then each computer on the hub gets an ip address from the modem. So, my server has a direct connection to the outside. Run ifconfig to get your internet ip address, then the world can get at your machine by
http://xxx.xxx.xxx.xxx You do not need a domain name yet. This address will change over time, but the reality is that the service providers change these very rarely. I have had the same ip address for 6 months.
When you are ready, buy and register a domain name, then find a dns service that allows dynamic dns, so you can change where the name points to when your provider changes your ip address.
If you are allowed only one ip, then set up a router, open the 'dmz' to point to the local address of the server machine, or open port 80 to point to the local machine. at 192.168.0.xxx. Then you find your ip address from the router, and proceed as above.
Stuart