you should have the content in your local files already. just upload them to the new site. as simple as that. if it is a blog, then you will need to backup the database, download the theme (if you dont have the theme files already), and when you are done setting up the new blog under the new domain, just upload the theme and import the database. pretty simple process actually
zip all file & folder in your root directory, copy or download zip file, export the database. in the new domain side, paste or upload the zip file, extract in the root, import database. change domain name in the configuration file ( if any).
And don't forget to redirect your old domain to the new one: lots of visitors will still know you by the old domain and you don't want to lose readership just because genuinely interested people couldn't find your site at the address they know!
Dear Buddy, This is something you need to proceed with very carefully. 1. Take the file and folder backup to your local machine from your original server 2. Take a database export from phpMYadmin to your local machine 3. Import file and database to new server 4. Make database changes to the required tables that for the URL values 5. change the nameserver from your new domain to this web hosting. now you need to be more clear when you say "move to new domain" If you want the website to appear on a new domain - all you need to do is remove the old domain's name server and place it in the new one's nameserver details through the domain cpanel. If you are talking about migrating a website from one web host to another, the above is the outline of the procedure. Further let us know the kind of website you are planning to move, is it a wordpress blog or some sort of dynamic cms etc? cheers Josh