I would offer some examples, to make this more concrete (although when I say concrete, I'm referring to something that fills my imagination with life and light, and gives me hope for the future of humanity).

CBT consists of two general branches, although in a more nuanced understanding they blend inextricably. These are cognitive techniques and behavioral techniques. Cognitive techniques rest on the premise that the bulk of our emotional reactions come from our interpretations of events, rather than the events themselves. For example, being snapped at by Brandon is a negative event for almost anyone. But one person might burst into tears and let it ruin his whole day, while another could shrug it off. The theory (which has extensive experimental evidence) is that the first person interprets the event as meaning something like "I'm impossible to be around, and I make everyone's life hell," while the other thinks "Brandon probably had a bad day." So, cognitive techniques focus on determining how one interprets events, looking for factual evidence to confirm or refute thoughts that lead to negative emotional states, and replacing those thoughts with ones that are realistic and contribute to good coping.

One example is the downward arrow exercise. In this, the user writes down the thought or idea that is making him unhappy / anxious / crazy, as nearly as possible. For example:

Making Brandon angry is terrible.

Then, he asks "what's so bad about that?" or "if that's true, what would it mean?"

That means that Brandon doesn't love me anymore

This continues...
That would mean that I'm a fundamentally obnoxious person
That would mean that I can't have friends or contribute anything to people's happiness

The goal is to get down to a level at which anyone would be despondent. Then we start at the top, questioning the observations and this links:

How can I tell that Brandon is even angry at me? I sometimes get annoyed at people when they haven't really done anything wrong, and I've seen other people do it too.
And even if Brandon is angry at me, that won't blot out all the years we've been friends. People have fights all the time, and then they get over it.
And even if Brandon does decide to hate me, that's his problem and not mine. There's a huge variety of people in the world, and if he doesn't like me that doesn't mean that no one else ever will.

So, what was once a prediction of doom becomes a more realistic observation, with checks and qualifications at every level of worst case scenario. Many people think that an analytic stance like this can't really help emotional problems, but the distance from the immediate maelstrom of emotions seems to be part of what helps. Over time, you can train your emotional outlook to be more like the healthy one described in the exercise, and feel this way without having to distance yourself from events.

The behavioral side of the discipline is based on the idea that familiar actions are easier than unfamiliar ones, and actions that have been rewarded are easier than ones that have been punished. One common exercise is "acting as if," or pretending that you already have the qualities you want. So if you want to be less afraid of dogs, sometimes it can help simply to pretend that you're not afraid of them, and do things that a (non-stupid) person who isn't afraid of dogs would do, such as walking by backyards that have barking dogs in them, or petting dogs on the street that are leashed and evidently tame. This is a form of exposure therapy and by itself will help you unlearn the disastrous predictions that lead to dog-phobia. Behavioral exercises also include simple reinforcement, as when a very shy person gives himself a reward every time he talks to a friend or meets a new person. The goal, of course, is not just to create an artificial proclivity but to undergo behavioral trapping -- that is, to encourage himself to do it enough that it becomes rewarding in and of itself, because having friends does have its own intrinsic rewards.