Drupal Upgrade Guide/Tutorial

Drupal Update Guide:
Back up site/ftp
Back up/export database - phpmyadmin
Note which modules you are using
Update modules to current versions for current drupal version prior to core drupal upgrade
Check to see that your modules are supported in next drupal version
Go to site status page
Run cron
Update database if necessary 
Switch site to default theme
Turn off clean urls
Disable all performance/caching
Turn off modules
Put site in standby/maintenance mode
Upload new drupal version files to server
Upload your old: 
Files directory
Any custom scripts, subdomain folders, custom themes
Go to yoursite.com/update.php
Download new versions of your modules then upload them to your site
Update previous custom theme to work with new version
Turn everything back on in reverse order
To be extra careful, update the database (update.php) after each set of modules you enable - you can check if its necessary on the status page.
permissions settings on directories
file system settings
image toolkit settings
rebuild access permission (if things are missing)
rebuild menu