(note: Joomla 3.0.1 will be released at approximately 9am PDT on October 9th, 2012)
This tutorial will show you how to update from Joomla 3.0.0 to 3.0.1, which is a bit different than normal.
If you use Joomla!'s FTP layer please see Note 3 below.
The update process is generally safe, but it's always a good idea to make a backup before updating. So please go ahead and make a backup of your site now.
If you have any difficulty installing from URL, download the file to your computer and install from there.
After getting the success message, go to Components >> Joomla! Update.
Note #1: If you are not getting the "Note: Hot patch for 3.0.1 update is installed" message, then please repeat Step 2 or ask for some help from a trusted developer.
Note #2: If you're not getting the "Joomla! update was found", click on Purge Cache button.
If you see both of the above, Install the Update.
Note #3: If you use FTP, you might have to FTP the update package, which you can download at: http://joomlacode.org/gf/project/joomla/frs/?action=FrsReleaseBrowse&frs_package_id=6517