Basic installation

The following is a simple guide to create a Drupal site in a few easy steps. You can also skip to the command line quick install guide for developers, read a more detailed version of these instructions, or check out the installation troubleshooting guide.
To follow these steps, you will need a SFTP client such as WinSCP or FileZilla, and a web server that meets a few basic requirements (e.g. a web server such as Apache, a database such as MySQL, and PHP.)
First there are steps for Drupal 7, then for Drupal 6 below. They are very similar.

Drupal 7

Step 1: Download

• Download the latest version of Drupal 7.
• You will get a file called drupal-x.x.tar.gz. Extract the Drupal files.
• Log into your server using your SFTP client and navigate to the web root directory. Upload all the files inside your drupal folder into the web root folder.

Step 2: Create a database

• Create a new database through your hosting provider's control panel. Make a note of the database name.
• Create a user, add that user to the database, and grant the user full rights on the database. Make a note of the username and password.

Step 3: Make the sites/default directory writable.

• For example, on a Unix/Linux command line, use this command: chmod a+w sites/default

Step 4: Install

• Browse to your new Drupal site. This will take you to the Drupal installer, which starts with: "Select an installation profile." Save and continue.
• Choose "Standard." Save and continue.
• Choose English or learn how to install Drupal in other languages. Save and continue.
• Choose the type of database you created (e.g. MySQL or SQLite). Enter the name of the database you created, the username, and password. Save and continue.
• On the site information page, you can set the site name and email from which the site will send out mail. You also set the username, email, and password of the first administrator account. Save and continue.
• Log in to your new Drupal site.

Drupal 6

Step 1: Download

• Download the latest stable version of Drupal 6.
• You will get a file called drupal-x.x.tar.gz. Extract the Drupal files.
• Log into your server using your SFTP client and navigate to the web root directory. Upload all the files inside your drupal folder into the web root folder.

Step 2: Create a database

• Create a new database through your hosting provider's control panel. Make a note of the database name.
• Create a user, add that user to the database, and grant the user full rights on the database. Make a note of the username and password.

Step 3: Create the configuration file

• In your /sites/default folder, you will find the default.settings.php file. Make a copy of this file and rename it to settings.php.
• Change the permissions on the /sites/default folder and the settings.php file to be writable. (On a Unix/Linux command line: chmod a+w sites/default).

Step 4: Install

• Browse to your new Drupal site. This will take you to the Drupal installer. Start filling out the form.
• When you get to the database screen, choose the type of database you created (e.g. MySQL or SQLite). Enter the name of the database you created, the username, and password. Save and continue.
• Change the permissions on the settings.php file to remove write permissions. (On a Unix/Linux command line: chmod a-w sites/default).
• On the site information page, you can set the site name and email from which the site will send out mail. You also set the username, email, and password of the first administrator account. Save and continue.
• Log in to your new Drupal site.

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Source: http://drupal.org/node/628292