The steps you need to follow depend on the version of Publisher you are using.
Unfortunately, Microsoft has removed the website design features from Publisher 2010 which would help you create a new site. However, a site you created in Publisher 2007 can be edited, updated and uploaded through Publisher 2010.
There are only a few web publishing resources available on the Publisher 2007 “Help-and-How-To” site, but this article has everything you need.
Prepare, publish, and maintain your Publisher Web site: http://office.microsoft.com/en-us/publisher-help/prepare-publish-and-maintain-your-publisher-web-site-HA010094760.aspx#BM2
Read specifically this section: Publish a website by using FTP
Microsoft is still maintaining the official “Help-and-How-To” site despite ending development or support for this program several years ago.
Prepare, publish, and maintain your Publisher website”
Specifically this section: “Publish to an FTP site” under “Publish your website”
There are a lot of other web-design resources available as well: http://office.microsoft.com/en-us/publisher-help/CH006357700.aspx
Regardless of the version of Publisher you use, you will need these settings to publish your site via FTP:
Website/Server: Your domain name, but without “www.” You may need to use this format: ftp://yourdomain.com (replacing “yourdomain.com” with your actual domain name).
Username: Your cPanel user name.
Password: Your current cPanel password.
Destination Folder/Directory: /public_html