Updating Packages
sudo apt-get update && sudo apt-get upgrade
This updates the package list and upgrades all the packages. You can use the -y flag if you hate typing yes. After the kernel and all packages are upgraded, this command should show you:
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded
Updating the Kernel
sudo apt-get update && sudo apt-get -y dist-upgrade
This upgrades your linux kernel distribution. These are regularly released. You can see which version you have by running:
uname -a
Updating the Firmware
sudo rpi-update
This upgrades the firmware as long as you have the Hexxeh script downloaded. It and instructions can be found here: https://github.com/Hexxeh/rpi-update