Sure there are a couple of parts to this. The first is your network connection itself, and the second is the software on your machine.
The machine part is pretty easy. OS X Tiger includes Apache, which is an industry-leading web hosting piece of software. You can also very easily get php and mysql going on your Mac to install any number of LAMP blog products (open source and otherwise).
To start up your web server go to System Preference/Sharing and active Personal Web Sharing.
If you machine is directly connected to the internet you are all set. If not, you need to open up port 80 on your router to point to your machine.
Now to the network connection. In order to get the outside world to see you machine users will have to enter in your IP address. The problem is almost all broadband connections are dynamic, meaning the IP address can change. There are a number of services out there that help alleviate this issues, one of the best is dyndns.org. For the fabulous price of free you can get a domain from them like mywebsite.unixrocks.com. They have a few domains like unixrocks, etc. available. Once you are registered Dyndns matches your IP address with your account and pushes any requests from the web to the address you have signed up with to your computer where your website is hosted. They even have a little app you can download that will ping Dyndns whenever your IP address changes.
There are other things to consider in setting up a home server, stuff like backup, power backup, and the fact that your connection is often shared (and that upload speeds are always slower). But for a pet project or a small site it can be a good way to go.
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