Well you have to start by knowing what you are running on your system. Once you figure out what you are running, its easy: you only need to read the ones that apply to a package you have installed. At first, you might check for the specific package on every security bulletin (on Redhat, this would be as simple as "rpm -qa | grep <package name>"). After a while, you'll get to know your system a lot better and know what to watch for.
Personally, I subscribe to the bugtraq lists and just scan the subjects every morning. If I see something that I have installed, I read more thoroughly. If it doesn't apply to me, I just skip it.
