By subscribing to the security alert mailing lists, and keeping
current, you can do a lot towards securing your machine. If you pay
attention to your log files and run something like tripwire regularly,
you can do even more.
A reasonable level of computer security is not difficult to maintain on a home machine. More effort is required on business machines, but Linux can indeed be a secure platform. Due to the nature of Linux development, security fixes often come out much faster than they do on commercial operating systems, making Linux an ideal platform when security is a requirement.