There's so many ways you can affect the tone of the story, and there are differences between conveying tonal shifts in a comic and in a novel.
Dialogue can change the tone of the story through introducing and releasing tension. (By tension, I'm not only referring to conflict, but the concept of making audiences anticipate something.) This can be done by having a character learn something shocking, or delivering the punchline of a joke that started out with an ominous tone.
You can use the environment to shift tones too. Films do this all the time, and I'm sure you're aware of what I'm taking about: Rain means gloom; a bright day makes us happy or easy-going; A dark alleyway makes us suspicious and scared. As you move forward with the story, you can use the environment as a mirror of the character's emotions and affect the story's tone.
When the tone changes, it's dramatic and the audience notices. But there's going to be a "baseline" where your story's tone lies most of the time, with spikes and dips happening periodically. To copy Sorrelyn's comment, a story's tone is going to be consistent for the most part.