Read the change log from your current version to the latest version that you are downloading.
While doing so, make sure all your current code will work without any bugs, even minor. Usually all updates are backward compatible. (But sometimes, if there are any major changes around a particular module, you will have a little rework in your code)
If the new version of ZF has a new feature that you can use for your site, modify your site to use it.
Update the framework in your development environment first (by pointing your lib path to the new framework files) and then make sure all parts of your site works the same and all your tests are passing.
Then update your production site with the new version using the same way mentioned in the question.