Just use these simple commands, in this order.
sudo apt-get update
sudo apt-get –with-new-pkgs upgrade
sudo apt-get dist-upgrade #updates linux kernel
sudo apt-get clean
sudo apt-get autoclean
sudo apt-get autoremove
For most setups this will work fine. There are other tools you can use ucaresystem, localepurge, gtkorphan, bleachbit, but these commands cover the basics of keeping your server up to date and go a long way towards covering basic server maintenance and keeping your system clean and up to date.