Debian uses packages called `.debs'. These can be installed using dselect (which is a front end to dpkg) or apt. I'm only going to mention apt.
Unlike other distributions on Linux Debian has a central repository for all it's .debs. There are different repositories for different Debian releases as well as local mirrors.
To update apt's list of packages you run 'apt-get update'. You can then install new packages or upgrade individual packages with 'apt-get install foo'. If you want to upgrade all the packages that apt has found newer versions of just use 'apt-get upgrade'.
To make sure that Apt picks up the latest security updates you want to
alter the /etc/apt/sources.list file before runging the 'apt-get update'.
For example if you are running potato then you want to add the line
deb http://security.debian.org/ potato/updates main contrib non-free
You may find that line exists and just needs uncommented.