What kind of website? WordPress, Static HTML, php,... If it is just a static html website you can just copy all your files to a new location and you will have a duplicate. With WordPress there are several options. The most easy way to do this is to export your blog (settings->export) and import the exported .xml on a fresh install.
Hello, I am not sure about the platform you have been using to host your sites. Panels like cPanel, Plesk, DirectAdmin etc will have a full account backup that can be used to replicate the complete account without much effect. However if that is not the case you will have to backup site files and DB and that should serve your purpose.