[ElDiabloConCaca]

Yes, you can do this. There are a few things you need to read up on:

1) Do you have a dynamically-assigned IP address assigned to you for your internet access, or do you have a static IP? You can find out by contacting your ISP, or possibly researching this on their website. If you have a dynamic IP address, then you'll need an account at a place like dyndns.org.

2) Are you behind a router (wireless, wired, etc.)? If so, you'll need to read up on "port forwarding" -- your router's manual will have information on how to do this with your router. Specifically, you need to forward port 80 to your Mac mini's local IP address.

3) Do you already have a domain name (i.e., "something.com") that you'd like to use? If so, you'll need to contact your registrar (or visit their website) and research "domain forwarding" -- specifically, you'll want to forward the domain to the domain name you signed up for in step 1 at a site like dyndns.org

4) After all this is done, you'll need to activate "Web Sharing" in the "Sharing" pane of the System Preferences on your Mac mini. You can read about how to create and serve websites on Mac OS X by visiting apple.com and researching the appropriate documents.

This should get you started -- if you have any specific questions or if you run into trouble researching this information, post back and we'll help to the best of our ability.