Not only is RET based on the idea that you can choose how to feel, another important aspect is that it's often not the experience that causes an emotion, but rather your thoughts and beliefs about that certain experience. The first rational question that mblumber mentions above is therefore very important.
Is my thinking based on fact?
Let's clarify this with an example. You're walking in the street and you see someone you know. You wave at the person, but s/he looks the other way and doesn't say anything. Depending on your thoughts about this experience, you could have several different emotional reactions. You could think: s/he is ignoring me! And that would make you angry. Or you could think: s/he is probably mad at me, and that would make you feel anxious or sad. You could also think: s/he is probably not paying attention and s/he didn't see me. That thought probably would make you feel amused at the most.
The reality is of course that often you don't know why that acquaintance doesn't greet you. Depending on which reason you think s/he has, your emotional reaction varies. This makes it possible for you to train thinking positive thoughts about the things that you experience, which makes you feel better.
Someone not greeting you in the street is of course not something to get very upset about, depending on who it is... But the same approach can be used for more complicated situations. If you often get uspet about the way someone acts, it can help to change your thoughts and expectations about that person. Often people have thought patterns that make it difficult to see the objective reality separate from their thoughts and beliefs. If that is your case, it can be very helpful to have a therapist ask you the Five Rational Questions and guide you through finding the answers.