Tone is a tricky one to figure out in a lot of ways. It's the kind of thing that can scare students off of English, I'll tell you what. In essence, tone has a lot to do with how a writer says something. Imagine a man screaming "I'm not angry!" Despite his words, his tone is telling you that he is, indeed, angry.
This works in a similar way in a story, but is a lot harder to figure out most of the time because you are not given such a simple scenario. You are given, sometimes, a whole ton of pages with lots of images and thoughts and feelings included. It can be easier to suss out in a shorter story than a longer one because sometimes the tone of a long novel can change as the book goes on.
To figure things out, you have to look at the types of words and images used in the story. Are you meant to be angry, depressed, sad, excited, amused? That can be a little hard to figure out, sometimes. It's not so much about what a character says as it is about how it is said.
Think about your average newspaper. It's formal and technical...no "tone." A tabloid is different...it is meant to "excite" and uses language to inflame the senses. An obituary is written very somberly.
Hope this helps!
Tone put simply, is the way a piece makes you feel or how the characters feel within a piece. Take for instance the book, "The Kite Runner". The entire book made me feel unclean. In the story a young Afghani boy watches while his servant is raped, kicks his servant and his father out their house for a lie, finds out that the servant is his illegitimate brother, and eventually redeems himself by saving the servants son, his nephew from being raped by the same man who raped his father. However, in the end, it is the nephew who saves his uncle.
The tone of the entire book is fear, deciet and loathing of one person for another. After reading this book, I found myself having trouble rooting for any of the characters until the very end. The violence, literally, left me drained and loathing a society that would put such burdens of class on its people.
Tone is the way a story causes you to feel or how it causes the characters to feel.