Often - sometimes several times a day - I see questions that open (or occasionally close) by apologizing for the poster's ignorance or for asking a 'basic' question.
Firstly, there's no need to apologize for ignorance here - the site exists to help us overcome our various forms of statistical ignorance; it's precisely what we're here for.
Secondly, there's no need to apologize even for a truly basic question; basic questions are actually likely to help many more people than the more esoteric ones, and some of our very best answers are thoughtful responses to what might be seen as basic questions. As long as you've put some basic effort into resolving your problem (at least check Wikipedia for definitions and search here to check if your question has already been answered), basic questions are welcome. In any case, seemingly basic questions are often surprisingly subtle - if you don't know enough to know the answer to a basic question, you probably don't know enough to know whether it's more complicated than it seems.
Is there a good place (perhaps the on-topic help?) where we can explain to users not to apologize for either of these things?
[Edit: indeed, it might be worth saying "don't apologize in your question" more broadly. If you're apologizing for something you can avoid, just fix it instead. If there's really nothing you can do about it, don't apologize for it.]