Upgrade using Magento Connect
In the admin go to System/Magento Connect/Magento Connect Manager
Paste magento-core/Mage_All_Latest into Paste extension key to install:, then click Install
You may get a message like this(and more) in the pear window below
magento-core/Mage_All_Latest requires package “magento-core/Mage_Core_Modules” (version >= 1.1.8, version ⇐ 1.2, excluded versions: 1.2), installed version is 1.1.6
At the far right of Manage Existing Extensions click Check for Upgrades
Rows of packages with available upgrades will now be yellow.
Chose the latest version in every rows select.
Now click Commit Changes.
Now again, paste magento-core/Mage_All_Latest into Paste extension key to install:, then click Install.