You'll need server software for a start. I use Apache server to test my PHP scripts locally, but it is possible to set it up to run as a server (in fact, pretty much every Unix based server in the whole world runs Apache). You'll have to get your nose into the documentation on that I'm afraid.
After that, you'll need to get the various components you wish to implement. Pretty obvious really - if you want to use PHP you'll need to download it's interpreter, etc. You should also start finding out a lot about security and get a firewall in place to stop the idiot script-kiddies screwing with it.
After that, create your site and your very nearly away. You see, at this point you certainly won't be able to access your site using the URL you specify: you can only access it with your IP address. To get the URL, you'll need to buy (well, rent) the URL from the various domain-name suppliers.
As Mark here says, you'll really have to have your PC on 24/7 in order for folk to access it. Your broadband connection will probably have enough bandwith to cope, but remember that you'll need some pretty nippy hardware to cope with all the people accessing it.
