With or without a domainname you can publish to the documents folder (the root) of the webserver or to the Sites folder in your Home directory.
Here's how I do it :
http://www.wyodor.net/Tutorials/iWebDemo/sFTP.html
You can use localhost or the name of your computer.
To use a domainname, make an A record, with a suitable subdomain such as "home", where you manage your domainname and point to the public IP number of your internet connection.
Configure your router to forward (port forwarding) to the IP number of your computer.
Note that you can have multiple websites on multiple server with the same domain name :
http://www.wyodor.net (a server in Denmark)
http://home.wyodor.net (guess where)
http://google.wyodor.net
http://blog.wyodor.net
And even free domainnames :
http://home.wyodor.net/dyndns/ (notice the changing of the URL)
btw, the home url is to a nas server upstairs. But it works with a desktop machine too.