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If you are a new drupaler (most likely if you are reading this), make sure to read drupal official handbooks as well as the beginner's cookbook. This tutorial is meant to complement those, which is based on mostly my personal experiences. I wrote this in the hope it could be useful to others. I don't claim myself to be a Drupal or Linux expert, so feel free to point out any errors.

If you are installing Drupal locally, for example on your home desktop, preferrably you have a linux/unix environment. It's doable on Windows, but probably doesn't worth the time. Plus, if eventually you want to find a public hosting company, most likely it'll be *nix based. If you don't want to convert to Linux at this time, you can either install Cygwin or VMware.
Regardless of which OS you choose, you'll need to have a web server (most likely Apache), PHP (Drupal is written in PHP), a database (most likely Mysql)
The default setting usually will work for you. One thing you may want to do early is setting the root password of MySQL, which is empty in default MySQL settings. This could pose a potential security risk to your server.

Set password:
$ mysqladmin -u root password NEWPASSWORD
You also need create a database for your website before you install Drupal
mysqladmin -u root -p create database_name
At the prompt, enter your password

Download the latest drupal from http://drupal.org/
Go to your www directory, which is /var/www/html in my case (CentOS), and extract the file by running
tar zxvf drupal-5.7.tar.gz

If you've already have a domain name, you may want to change the directory name to your domain name, e.g. mv drupal-5.7 example.com
now you can access your new site by
http://localhost/example.com
or
http://example.com (if you've already setup the DNS server)
If you see this
Add write permission to settings.php as required by Drupal
chmod g+w settings.php
Then You should be able to enter all the database information

If you see this: then congrats! you just have installed Drupal! Go ahead and take a look at your new drupal site:

Lastly, don't forget to remove write permission by running
chmod og-w settings.php.