Check the Redhat Updates and Errata frequently, or sign up for the Redhat Network using rhn_register (There's usually an icon placed on your desktop), and use up2date to automatically update your system. Redhat 7.3 and above includes by default an update notification applet in the Gnome Panel. Important notifications are indicated by a flashing red exclamation point. Always read notifications and take the necessary action.

Use ntsysv (also accessible from within setup) or serviceconf (requires X) to shut down services you know you don't use. Don't shut a service down if you don't know what it is. It might be important. Definitely don't turn one on if you don't know what it is. Unmanaged open resources pose a huge security threat. In addition, you can uninstall packages you don't need. Even better, don't install them to begin with. Avoid custom and everything installs unless you know what you're doing.

Use lokkit (also available from within setup) or gnome-lokkit (requires X) to prevent access on ports you don't use. If you don't know anything about it, a medium default setting is good. You can customize the settings to your needs if you need access to certain ports (such as if you run an ssh or web server) Recent versions include firewall setup as part of the installation. Use it wisely.