You will need to provide a database for your drupal installation.  

This assumes you have some knowledge of MySQL, and already have it
installed and configured. If not, please refer to the Gentoo MySQL
guide at the following URL:

https://wiki.gentoo.org/wiki/MySQL/Startup_Guide

Once you have a database ready all you need to do is to go to this 
location

http://${VHOST_HOSTNAME}/${VHOST_APPDIR}

and provide the credentials required for the database access.

If you installed into a vhost, for the above address to be accurate,
you need to pass -h "<host>" and -d "<install dir>" into webapp_config.
The protocol is hardcoded, so you'll have to use https:// if you're
using an SSL / TLS connection.

SECURITY NOTICE: If you use SSL on your Drupal installation, you
should enable the PHP configuration option 'session.cookie-secure'
to make it harder for attackers to sniff session cookies.

References:
CVE-2008-3661
http://www.php.net/manual/en/session.configuration.php#ini.session.cookie-secure
http://drupal.org/node/315703

To run Drupal on a web server[1] other than apache, one needs to do
some work, mostly related to adding the configuration in the .htaccess
files to the web server config files and enabling redirection.
For lighttpd you may want to check [2][3] and for nginx [4][5].

 [1] - https://www.drupal.org/requirements/webserver
 [2] - https://groups.drupal.org/lighttpd
 [3] - https://www.drupal.org/node/43782
 [4] - https://www.drupal.org/node/1030854
 [5] - https://www.nginx.com/resources/wiki/start/topics/recipes/drupal/

PHP-FPM also supports user.ini files with per-directory settings[6].

 [6] - http://php.net/manual/en/configuration.file.per-user.php

After that you can start to use drupal.