I find the update workflow always very difficult in Magento. Most likely I'm not doing it correctly ;) I go to the Magento connect manager. I hit the 'Check for updates' button. After a while I see new versions of the packages are available. I'm especially interested in the Magento Core updates so I select 'Mage_All_Latest' which is now at '22.214.171.124 (stable)' and select '126.96.36.199' in the select box. Now I click the 'Submit changes' button and I wait. The progress box is filled with messages about lib_* packages and other core packages not compatible with '188.8.131.52'
Isn't this the appropriate work flow? If not what is the use of the Connect Manager? I remember having the same issue when upgrading from 1.9.1 to 184.108.40.206 but evantually got it working. I don't remember how it did that, though ;)