1) Non- Programmers
For non programmers or non administrators easy way to upgrade wordpress is using auto-upgrading plugin.
Download this plugin from: http://wordpress.org/extend/plugins/wordpress-automatic-upgrade/
Unzip the files into your wp-content/plugin directory and activate the plugin. Go to manage menu and run automatic upgrade. It will do the rest !!!
2) Normal Programmers / Administrators
Login into your server via putty or ssh and go to your root/www directory. (I am explaining the linux server here)
wget http://wordpress.org/latest.zip unzip latest.zip mv ./wordpress/ /path/to/www/root
It automatically replace all files and maintain all of your old themes and plugins. When you take wp-admin it automatically asks for database upgradation. Just do that. Enough, your new wordpress is ready
3) Very Simple Way (for Administrators )
Use wordpress svn while installing wordpress.
and when new wordpress upgrade comes, just do
Enough your new wordpress is ready in a single line .