This presumes that you will install drupal 6 in /var/www/drupal6/

Prerequisites

apt-get install apache2 php5-mysql php5-gd libapache2-mod-php5 mysql-server

Configure httpd.conf by adding a ServerName line

ServerName localhost

Start apache

sudo /etc/init.d/apache2 restart

Create the database

sudo mysqladmin create drupal6 -p
sudo mysql -p

Configure database permissions

sudo mysql -p
use drupal6
GRANT SELECT, INSERT, UPDATE, DELETE, CREATE, DROP, INDEX, ALTER, CREATE TEMPORARY TABLES, LOCK TABLES ON drupal.* TO 'drupaluser'@'localhost' IDENTIFIED BY 'drupalpass';
FLUSH PRIVILEGES;
exit;

Allow the installer to write to a portion of the installation directory

chmod 777 /var/www/drupal6/sites/default

Run the installer; browse to http://localhost/drupal6/

resecure the portion of the installation directory

chmod 755 /var/www/drupal6/sites/default