Tested with Ubuntu 16.04 (Xenial) LTS and Zabbix Server 4.0 beta 1 on September 2018

Add Zabbix 4 repository (beta is version still numbered as 3.5)

echo "deb http://repo.zabbix.com/zabbix/3.5/ubuntu xenial main" | sudo tee /etc/apt/sources.list.d/zabbix4.list > /dev/null

Add the missing public key for repository with

sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys 082AB56BA14FE591

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

mysql_secure_installation

default answers (see below) are fine for a normal setup

Enter current password for root (enter for none): --> should be empty, just press Enter
Set root password? [Y/n] --> Y
Remove anonymous users? [Y/n] --> Y
Disallow root login remotely? [Y/n] -->  Y
Remove test database and access to it? [Y/n] --> Y
Reload privilege tables now? [Y/n] --> Y

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