For the impatient, here is a basic outline of the installation process, which normally takes me only a few minutes:
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Move the Moodle files into your web directory.
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Create a single database for Moodle to store all it's tables in (or choose an existing database).
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Visit your Moodle site with a browser, you should be taken to the install.php script, which will lead you through creating a config.php file and then setting up Moodle, creating an admin account etc.
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Set up a cron task to call the file admin/cron.php every five minutes or so.
For more information, see the INSTALL DOCUMENTATION:
http://docs.moodle.org/en/Installing_Moodle
Good luck and have fun! Martin Dougiamas, Lead Developer