Various parameters may lead to you or your group wanting to host your web site off campus. These include:
AND: Your site does not include sensitive or personal university data.
In these cases you will need to find a commercial server.
First come up with a domain name and check that it's available. Most hosting companies will register your new domain name free. Each year you will need to renew that domain name (your hosting service will remind you when it's time) and that renewal is done by the hosting company and generally costs about $10 per year. Note that you cannot get .edu domains, but .org and .com and .net are available.
After you've determined your url is available, it's time to find someone to host it. Here are some considerations and options when selecting a hosting company.
You will be provided access parameters by your hosting company. They usually will also provide CPanel or some other web-based set of tools for uploading, looking at site email, adding domains, etc. However you may also want to use an FTP tool such as File-Zilla for large transfers and site maintenance. If you are using Adobe Dreamweaver or other professional web editors, an FTP tool is built in.