If you wanna have your own physical server, you obviously need a server to start with
A dedicated box would be the best, an old 486 running Linux will probably do fine unless you're coutning on heavy access.
Set it up with Linux/Apache, thats free, then you need a permanent internet connection(well no not really, but not having a "real" connection for a server is a bad idea).
Thats pretty much it, I guess the internet connection part would be the hardest part, but if you have some sort of broadband connection and the provider allows servers, that problem is solved, a broadband connection will most certainly be sufficent.
Of course this is just a very quick howto, there are more details involved.
For Linux/apache stuff, have a look at these links:
Linuxdoc.org
Apache.org
Linuxnewbie.org
Or throw me a pm or mail.