The following is what you will need to do to get your website up and online.
1. Obtain 3rd party FTP hosting (Linux) account.
2. Obtain a domain name for your website if you didn't already have one. If you did you will need to redirect the domain name to your website's new location on the FTP server.
3. Publish your website directly to the FTP server (iWeb 3) or to a folder on your hard drive (iWeb 2) and use a 3rd party FTP client like YummyFTP, Transmit or Cyberduck to upload the web folder and external index.html file to your root folder on the server.
The following provides additional information on alternatives for the MobileMe feature that have been discontinued and information on hosting servicesApple ‘iCloud’ - Pertinent Questions - Roger Wilmut
Tutorial iW13 - Easily Transfer Website Folders From MobileMe to a 3rd Party Server
Tutorial iW14 - Modify iWeb So Popup Slideshows Will Work After MobileMe is Discontinued
Tutorial iW16 - Using HostExcellence.com
iCloud/iTunes in the Cloud/Apple ID's: This is how it works/What people don't understand
MobileMe: About moving to iCloud
Frequently asked questions about the MobileMe transition and iCloud
Creating an iCloud account: Frequently Asked Questions
iCloud: MobileMe services that no longer sync after moving to iCloud
Apple IDs and iCloud
I’ll add other sites to the list as I come across them.