In order to "host" a local website you have to install a web server on your machine. I am pretty sure Leopard comes with Apache already installed. Apache is perhaps the most commonly used server in the world so you can rest assured that there is a lot of help out there. Getting a localhost instance up and running on a local machine isn't hard, but it would be more than I could really cover here. Here are a couple of links to get you started:
http://www.onlamp.com/pub/ct/49
http://www.google.com/search?hl=en&q=+site:www.onlamp.com+Apache+Mac+OS+X
http://www.devarticles.com/c/a/Apache/Using-Apache-and-PHP-on-Mac-OS-X/
http://www.apple.com/server/macosx/features/webhosting.html
A good option for a complete local development environment is XAMPP which installs Apache (web server), MySQL (a rational database), PHP or hypertext preprocessor (a scripting language) and Perl (a scripting language).
http://www.apachefriends.org/en/xampp-macosx.html
As far as your domain is concerned, you might not want to point your URL to your local box unless you are intending it to be a server. That would pose a security issue and I am not sure your ISP would appreciate your bandwidth usage.
Once you have apache set up, you can open your trusty web browsers up and point it to http://localhost or http://127.0.0.1 to see your locally hosted web pages.
You are on your own for Dreamweaver, that's commercial software and I am sure there is a Mac version. As far as I know, Dreamweaver has native support for HTML (hypertext markup language) and PHP (hypertext preprocessor) both of which are installed by default on OS X. Good luck and I hope you have fun!
You might want to consider checking out Ruby on Rails for web development. It's fast, easy, powerful, well supported, and the wave of the future!