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.