If you own the files, you can use Filezilla or another FTP client to access your server and download the source files. Once you have the source files you can then upload them to any other server you want.
You will need the following to connect with filezilla:
- IP address of your website/webserver
- FTP username and password (usually setup and defined by you in your cPanel or there may be a default account)
- Port number to connect with (22 for hostmonster)
Keep in mind you will need the entire site for it to function properly.
If your site is feature rich and filled with advanced coding, you may need to migrate a database and adjust settings at the new domain to get it working.
Yours looks like its mostly html/css and javascript, so the contents of the public_html folder should be all you need.
Connecting to Your Hosting Account with FileZilla (FTP)