Its Simple !
1. Login to your Cpanel -> File manager ->zip the entire FTP content, Download it to your local machine.
2. Go to PHP MYadmin -> export your MYSQL database
similarly go to your new host.
1.Upload the files to FTP.
2. create new database with the same name and import/ restore the backed up database
Thats it in short.
Do a google if you want screenshots on the above steps, also ask me questions if you have any.
Josh, OrangeCopper solutions