I have an iWed designed website which I can't up=date. I want to design a new website with a different place (everweb?) How do I get rid of the current site? I want to use the same domain name.

So, You want to delete the present website. That's correct?
If so, you can do it trought accessing to the website "administration panel" or via "FTP".

A Adminstration Panel (or "admin panel") is a website that your host /domain provides to You, where You can edit everything you want - the same is for the "FTP", "FTP" is a server where you access to Your website and edit what you want, and that includes delete the current website.

Any questions please ask.

So, if you want to remove your old iWeb site and re-build it with EverWeb, then you need to go to your web host where your site is hosted and you need to connect to it with an FTP application such as Cyberduck, or Transmit or Yummy FTP or something similar. You then need to get the settings to allow you to connect to your hosting and once there, you can see all the files on your server. Delete these iWeb files from your server and once you have finished building your new site with EverWeb, upload the EverWeb files to your server instead and your new website will be live.