Or if you want to run a website directly from your PC try
www.no-ip.com
Of course, your PC will have to be on all the time. The advantage is that you'll have masses of web space (whatever your PC supports), it's utterly free, you can choose whatever name you want and provide whatever services you want.
For hosting, go to: www.frihost.net, keep active on their forum and they will give you free hosting (sorry mods if this wasnt allowed).
For a domain, go to www.dot.tk, I personally don't like this domain, but it's free, and is quite simple to use I think. If your looking for webdesign programs, then PM me about it as I'd rather not discuss things publicly, and it will take me forever to type things up. If your a begginer, then go to www.freewebs.com, that host gives you the ability to make a website without using one bit of HTML, but they don't look as good. I have a website up and running, but it's a very temporary homepage, and i'm creating my new one on a program called DreamWeaver, if you want more on that, feel free to PM me!
It depends what you want to do. Google are trialling a new hosting service which allows you to build up a site, but it's quite limited as to what you can do.