This section is intended for those who have not previously dealt with the security implications of having a full-time Internet connection. Or may not understand some of the basic concepts of security. This is meant to be just a quick overview, not a comprehensive examination of all the issues! Just enough to give you a gentle shove in the right direction. Please see the Links section for sites with more details. Also, your distribution surely has plenty of good information as well.
Take passwords seriously, using non-dictionary "words". Use shadow passwords (this should be a standard feature of newer distributions). Do not allow remote root logins. See the Security HOWTO for more details and ideas.
Use ssh instead of telnet or rsh.
Set up a firewall to limit access, and log connection attempts. This will be different depending on which kernel series you are using: ipfwadm for 2.0, ipchains for 2.2, and iptables for 2.4. See the below HOWTOs for a more in depth discussion on this and other security related topics:
Security-Quickstart-HOWTO and for Redhat based distros Security-Quickstart-Redhat-HOWTO
Additional references are in the Links Section below.