First you will have to purchase website hosting from one of the many hosting sites available. Next purchase a domain name.
Then if you have iWeb 3.0.4 you can obtain the FTP information from customer service of your web hosts, enter it into iWeb's FTP window and publish to the new server.
At your domain name provider forward the domain name to the location of your website.
Some hosting services offer both domain name and hosting in a package like HostExcellence.com.
This may be of help to you: Life After MobileMe.
You will need a 3rd party web host to upload your websites to. Depending on the version of iWeb you are using you have a couple of publishing options:
iWeb '09 (3.0.4) you can publish to an FTP Server or a local folder. ( With the built in FTP in iWeb you will end up with an address like "www.YourDomain.com/sitename/Home.html )
iWeb '08 you can publish your website to a local folder
I have been using IX Webhosting for several years with little to no problems "usually the problem was something I did" and they have been quick to solve any issue I have come across. The have plans that start at $3.95 a mo (USD) and their customer service is top notch.
"I may receive some form of compensation, financial or otherwise, from my recommendation or link."
If you used a personal domain name with your MobileMe site you will need to contact your domain name registrar and get it pointed to the files on the new server by entering the nameservers.
If you didn't have a domain name, most hosting services will give you one for free...
Republish your site...
..and make sure you redo the SEO so that we can find it...