Edit /etc/apt/sources.list.d/zabbix.list and paste the following lines

deb http://repo.zabbix.com/zabbix/2.2/debian/ wheezy main contrib non-free
deb-src http://repo.zabbix.com/zabbix/2.2/debian/ wheezy main contrib non-free

Then add the gpg key

gpg --keyserver keys.gnupg.net --recv D13D58E479EA5ED4
gpg --export --armor D13D58E479EA5ED4 | sudo apt-key add -

and update the apt package list with

apt-get update

Install the Zabbix server (if mysql has not been installed before, please note down the root password!)

apt-get install mysql-server zabbix-server-mysql zabbix-release

If everything went well, we can also add the Zabbix Web UI (not needed but really, really useful) with

apt-get install zabbix-frontend-php

Now edit /etc/apache2/conf.d/zabbix, uncomment the date.timezone line and set the correct timezone. Mine looks like

  php_value date.timezone Europe/Rome