To host your own webserver you need to have a Static IP Address assigned to your PC/Server. This is set up by your ISP - at a fee! So contact your ISP and ask them about setting you up with a Static ISP. When you have one you can then access your PC using that ISP. You should research (heavily) the security implications and setting up IIS to allow only authorised traffic to authorised pages/folders/content etc.

You still can host even if your IP is dynamic. Last time I tried http://www.dyndns.org to host my own server. It's pretty good and free. But you can only get subdomain. For domain, you have to check it out. You might want to take a loot at there.

Hope it helps.