This method will disable root logins from remote connections to this computer. Remote connections are initiated using the telnet or ssh protocol and allow a remote user to control your computer in the same way that a local user would. Disabling remote ssh logins is a very smart thing to do since a lot of Linux users are attacked by hackers who try to brute-force root passwords using ssh.
To disable root logins through ssh, edit the file /etc/ssh/sshd_config. Refer to your distribution's documentation in case the location of the file is different in your distribution. In this file, change the line that says "PermitRootLogin yes" to "PermitRootLogin no". If there is a # at the start of the line, remove it. Now save the file.
This hole might already be plugged in your specific distribution by default, but it doesn't hurt to check. Once the file has been modified and saved, you must restart the ssh daemon to use the new configuration. To do so, type "/etc/init.d/ssdh restart" to make it use the new configuration file.