How should I explain the effects that a passage has on its reader?

It's often much easier to work out what a passage makes you feel than how it has that effect on you, it's reader. An easy structure to remember to help you with this is P-E-E (Point-Example-Explain). 
First off, work out what the passage is making you feel. You don't have to think too hard about this (in fact, it's often easier when you don't think hard): does it make you feel sad, joyful; does it remind you of feeling in love, or feeling angry, or excited, or frustrated? This feeling becomes your Point.
Now that you have your point, find a line or phrase from the passage that seems to really to encapsulate this feeling. Again don't think too hard: what line do you find most moving; what phrase seems particularly sad or angry or joyful? This becomes your Example.
Once you have both your Point and your Example, now you have to work out what it is about that phrase or line that you find so moving. This is where you have to start thinking analytically. There are lots of different ways that a quotation an affect an emotional response; broadly they can be split into linguistic and stylistic (or, put simply, the language that is used and the way that it is used). //Here we would talk about some specific literary devices and how, specifically, they affect that emotional response in a passage relevant to the pupil's syllabus.//
Now that you have your Point, your Example, and your Explanation, you can knit them together into a cohesive paragraph to use in an essay or exam paper. //This would lead on to a discussion of some of the specific stylistic pitfalls to avoid here, e.g. use of the first person, beginning sentences on prepositions etc..//