There have been reports of this actually taking less than five minutes, but we're not responsible for the installation being easier than it should be.
wp-config-sample.php and fill in your database details. Save and rename the file to wp-config.php.wp-admin/install.php.That's it! At the end of the installation it will give you a login and a random password. The password is random, so be sure to write it down or at least copy and paste it. Once you're logged in you can change the password.
If you want to let others know about your new WordPress powered site, you can announce it in the forums.
If you run into any problems, check out Common Installation Problems.