The easiest way to do this is by comparing your theme files.
You will need to use a file comparison software like Win Merge (kaleidoscope for Mac, Meld for Linux).
This ensures that you aren’t caching maintenance pages during the updates and are not otherwise interfering with the update process.
Often, Word Press updates are accompanied by plugin and theme updates.
If you remember the changes you made to your theme, then simply copy and paste the code snippets from old theme to the new version.
On the other hand, if you do not remember the changes you made, then you will have to find them first.
Before upgrading you should activate the Classic Word Press theme that was bundled with versions 1.2.x and prior.
I want to update a class library (a single DLL file) in a production web application. I read an answer on Stack Overflow (sorry, can't seem to find it anymore because the Search function does not work very well), that led me to believe that I could just paste the new DLL in the bin folder and it would be picked up without problems (this would cause the WP to recycle, which is fine with me because we do not use In Proc session state).
However, when I tried this, my site blows up and gives a File Load Exception saying that the assembly manifest definition does not match the assembly reference. Updating the DLL in Visual Studio and re-deploying the entire site works just fine, but it is a huge pain in the rear.
It is worth noting that backing up the uploads folder (inside wp-content), which can often take a long time, is not necessary before upgrading.
We have backups of it on hand, plus nothing in a Word Press update is going to affect your uploads. In most cases this will be W3 Total Cache, Super Cache, or Quick Cache.