Here are the detailed steps I used.
0. Login as admin to your joomla site and take the site off line, be polite and give a good estimate of when you will bring it back on line in absolute terms like 11:00 am Sunday June 11, 2006.
1. Check your current installed version System->System Info->System Info tab. Check the joomla version line. Log out of joomla admin.
2. Get the patch file for your version to 1.0.9, I use the tar.gz format.
3.Backup your system
4 Upload the patch file with cpanel to your Joomla root directory for me public_html/joomla. The patch assmes it is unpaced in the joomla root directory.
5. For safety I copy my joomla directory with the patch to my /tmp directory with cpanel, then I use cpanel to extract the files from the tar.gz by selecting the tar.gz file and hitting extract. This ran without errors and then I used gftp (linux ftp gui) to check the file owner ship and permissions of a few random directories and files in the updated joomla tmp agains those in my offical joomla directory. They all looked good.
8. Used cpanel to extract the patch in my official joomla directory.
9. Logged back in as admin and check the version as in step 1, it should be 1.0.9 now.
10. Enable the site, hit some of your custom modules etc and generally surf the site.