Does your friend have a fixed IP address with his ISP? If not then your really going to be complicating the process since you will have to sign up and configure a dynamic DNS service.
To host on a home computer you need a DNS service to have your dns entries. To do this I would suggest you sign up for a free account at
www.zoneedit.com This is where you match the server IP address to the domain you want it to serve pages for.
You then put the zoneedit DNS server entries into your domain registry.