You need to republish your website fron iWeb...
... to a new hosting service...
Then contact your domain name registrar and get the domain name forwarded to the new host.
This video tutorial will walk you through the steps of getting your iWeb site on another server.
What do you mean "how do I find my old website domain name/address?"
Do you need to know which company you purchased it from? Post your domain here and I can find out.