If you just want it to work locally (for test purposes maybe), just add the appropriate line to your hosts file.
If it is local, this should work:
127.0.0.1 \t hosted.allowee
where \t is an actual tab character (typed with the tab key).
In Unix (Mac OS X included), you can find the hosts file in the /etc directory. On Windows machines the file will be under either the Windows directory, or the WinNT directory, if memory serves me. This of course depends on what version of Windows you are using.
If you actually need your site to be available on the Internet, I would suggest using a free or donation based DNS such as dyndns.org, or perhaps one provided by your domain name registrar.