First you'll need web space.
One option is to stand up your own site on your own (sort of - you "rent it") server.
You can purchase your own domain name (
www.crazypokemonswebsite.com, for example) from places like godaddy.com or namecheap.com (my preference).
Secondly, you need webspace. Both of the above places off web hosting. Lots of others too (including Yahoo and the one I use, telnap.com (but I don't recommend them)).
Once you have the name and the server, you put up whatever you want people to see.
(There's obviously more to it than that, but that's what you need to get started.)
I believe that Yahoo, GoDaddy, and Namecheap will help walk you through it.
Another option is (as Charlie pointed out) Wordpress and services like them. (I don't know a lot about them, so I defer to others.)