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)

type:

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.

svn co http://svn.automattic.com/wordpress/trunk/

and when new wordpress upgrade comes, just do

svn update

Enough your new wordpress is ready in a single line .