William Stearns has a good write up on Linux security tips for first time Linux users.

Here are a few:

1. Set up regular updates for your particular Linux distribution
2. Lock your system when you step away from it. To lock the Gnome graphical desktop, run the following command, part of the “gnome-screensaver” package:gnome-screensaver-command –lockFrom a text console, run this, part of the vlock package:vlock -aFor KDE, right click on the desktop and select “Lock Session”. In Ubuntu, press Ctrl-Alt-l (the letter “Ell”, configurable in System/Preferences/Keyboard shortcuts). All require the password of the logged-in user to continue work.
3. Do your day-to-day work with a non-root account. When you need to do root-level tasks, become root with “sudo” or “su” long enough to do the task (alternately, log in as root on a text console for this task). http://www.stearns.org/doc/sudo.current.html

Go check out the rest of the tips.