Unless you are specifically paying extra for a Static IP address, it's probably assigned dynamically by your ISP. Getting a hostname is only half the battle; once you have it, you have to associate it with your IP address. If your IP address keeps changing (i.e. a dynamic IP) then it can be difficult. Also, many residential type ISPs (Rogers, etc) don't permit you to associate a hostname to your IP, precisely because they don't want you to run a server on their 'residential' system. They'd much rather you pay $$$ to use their 'business' service instead.
Anyhow, there are lots of ways around this. There are lots of companies which offer solutions to track your dynamic IP address. I use one called DYNIP (
www.dynip.com). It's pretty cheap, you install a wee little program on your computer, and as long as it's turned on and connected to the internet, people can find your server. You pick your own user name then stick their name on the end of it, like this: va3uxb.dynip.com
If you want to have your own domain name (without the dynip or whatever) you can do that too, but it costs more -- first you buy the domain name from somebody, then you go to a company like dynip and use their service, and they associate your domain name with their tracking software.
It works quite well. You can connect to my home web server and view the Apache test page here:
http://va3uxb.dynip.com:8080/test/
Of course, if you have a static IP address then you can skip right to the domain-name part. There are a zillion companies out there who will hook you up with a domain name - they're cheap enough, I have 3 or 4 of them myself.
There's a lot of other things to consider of course, like your router will have to be configured to allow access on whatever service port(s) you are using, and to direct that traffic to your web server. In my case I have web access enabled through my router and into my B&W serve on port 8080. (Usually it's on port 80).
Still, it's pretty easy to get up and running. It was easier to install and configure Apache to do what I wanted on my Macintosh than it was on the Linux servers at work.
-Stephanie