A few assumptions:
1) Lighttpd and Mysql is already installed and configured on the system and admin passwords are in hand.
2) PHP5 is also installed on the system
3) Lighttp and mysql daemons are up running before installation.

As of 26th Nov, 2010, Zabbix 1.8.2 is available from ubuntu repositories.

1) From synaptic or using apt-get, install zabbix-server-mysql and zabbix-frontend-php.
2) While installing, package manager asks for admin password for mysql and creates a database by name zabbix. Later on asks you for a new password for database zabbix. Remember this password with care.
3) After this, zabbix-frontend-php will also be installed.
4) See if zabbix-server daemon is up. (ps aux | grep | grep zabbix).
5) Now that it is installed, one needs to change time zone in php.ini (/etc/php5/cgi/php.ini - on maverick). You should be looking at "date.timezone" in php.ini. Entry should be something like this: date.timezone =Asia/Kolkata in php.ini. For setting a different zone,  look at this page first before setting: http://in.php.net/manual/en/book.datetime.php.
6) Edit following entries in php.ini
max_execution_time (better be 300 or above), memory_limit (better be 128M or above), upload_max_filesize ( better be 2M and above).
6) After changing php.ini, restart/reload lighttpd daemon.
7) By default, zabbix server start at port: 10051. Add following lines to /etc/services:

# Zabbix ports
zabbix_agent 10050/tcp
zabbix_trap  10051/tcp

8) Edit "DBPassword" entry in /etc/zabbix/zabbix_server.conf and add the Zabbix db password that was created at the start.
9) By default, zabbix-frontend-php installs in /usr/share/zabbix. You can edit lighttpd.conf (/etc/lighttpd/lighttpd.conf) and point to /usr/share/zabbix or copy /usr/share/zabbix folder to /var/www.  What I did was i created a link to /usr/share/zabbix in /var/www. That also works.
10) Launch your browser, point to http://localhost  or http://localhost/zabbix (as per your zabbix installation)
11) If every thing goes well, you should see a launch page as shown in
12) If this is what you see, then your installation is complete.
13) Suppose if you see this page, then your installation is not yet completed, follow the steps and installation be done in simple steps.

14) If you have any problems, you can mail me the problems in installation.