Download drupal from http://drupal.org/download

I prefer drupal-6.20 to drupal-7.0. Download any version of your choice. (say drupal-x.y)

Extract the tar file. You get a folder named drupal-x.y.
Rename drupal-x.y/sites/default/default.settings.php to drupal-x.y/sites/default/settings.php
Create a directory named sites under /var/www/html
Move the folder drupal-x.y to /var/www/html/sites

Create a new database for your site.

mysqladmin -u username -p create databasename

Log in and set the access database rights:

mysql -u username -p

GRANT SELECT, INSERT, UPDATE, DELETE, CREATE, DROP, INDEX, ALTER, LOCK TABLES, CREATE TEMPORARY TABLES ON `databasename`.* TO 'username'@'localhost' IDENTIFIED BY 'password';

FLUSH PRIVILEGES;

Run your apache server and mysql server.

service httpd start
service mysqld start

Now open http://localhost/sites in your browser.

Click on drupal-x.y. Follow the instructions provided there and complete your installation.