Step 1.
Copy site files via FTP manager and export database useing phpmyadmin. To do this see also http://www.joomlahow2.com/how-to-backup-joomla-site/ . If you copy files to localdrive you will need to upload files to new server, also using FTP manager.

Step 2.
Import database using phpmyadmin. In phpmyadmin click on Import.

Browse for your database and click on Go button.

Step 3.
Modify configuration.php file and  set the new values.

$host – Usually it is se to “localhost”
$user – This is a name of your database user.
$password – This is the database user’s password.
$db – This is the database name.
$tmp_path – absolute path to the tmp directory on your server, for example  “/root/site/joomla/installation/tmp.”
$log_path – This is the absolute path to the logs directory on your server, for example “/root/site/joomla/installation/logs.”
$live_site – URL of your site. For example “http://www.joomlahow2.com”.

Go to default template folder on server or local drive. Default template is template  that is currently being used. In this folder just replace favicon.ico with your icon. If there is no favicon.ico try to paste your icon in this folder and look for small icon in Web Browser. Your icon should be there.