First login to your Debian system as root and execute "apt-get update" at the shell prompt. Information will be output on your indicating that sources for updates are being accessed and when complete the message will be displayed as follows:
Reading package lists... Done
After the updates have successfully been downloaded, execute "apt-get upgrade" from the command line to update your Debian OS to the latest available software. During the update process questions may be asked for some of the software being upgraded due to significant configuration or OS changes. If questions are asked and the update process pauses you will need to make the appropriate response based on the options given in order for the update process to proceed.
After all updates have been applied it is recommended that you perform a soft reboot of your server using the "shutdown -r now" command from the command line prompt. This is to ensure you boot into any new kernels that may have installed during update.