You will need to backup all your files from the original website. For instance if your website is in /public_html you will need to backup all that files, in that case the best is to generate a compressed file like a gzip in a non public directory (/home for instance). Then you will also need to backup your MySQL database and for that you can use the command line or phpmyadmin.
You will have more easier ways to do it if you are running cPanel where you can generate a full backup then just restore it in the new server. You will need to update the database connection information in the app/settings.php file.
If you feel comfortable with SSH you can use rsync command to move all the contents from server to server directly, then import the .sql to the new server sql.