You can do minor upgrades like 2.3.2 to 2.3.3 with quite a lot of confidence, however, you are right to want to have a QA process in place.
The basic approach is to apply the upgrade to a copy of your real site, and then test that the upgraded copy is working OK by clicking through some pages, and verifying that the functionality that you really care about sitll works.
You need to think about who is going to actually do that, how much time then will have available, and whether they are the sort of person who needs a very rigid set of testing instructions, or whether they would be better of with something more open-ended.
In either case, it is a good idea to try to build up a list of what the Moodle features you really rely on are, and focus your testing in those areas. For example, if you know that quiz X on course Y contains all the different question types that anyone uses on your Moodle site, then that would be a good quiz to test as part of the upgrade, because if that works, probably all the other quizzes work too.
A major upgrade like 2.3.x -> 2.4.y is a much bigger deal. There may be significant new funcitonality, so as well as just testing that the site works after the upgrade, you may also need to announce the changes to your users. In any case, you should read the relevant release notes: http://docs.moodle.org/dev/Releases, to get a feel for what has changed in each release.
