Switchcraft’s story is told through chapters, which you can find by tapping the Mirror icon in the middle of the bar at the bottom of your main screens. You can see how far along in the chapter you are by checking the progress bar on the left side of the magic mirror screen.
Each chapter consists of multiple tasks that you complete to advance further in the story. Next to each available task in the magic mirror, you will see how much magicka you need to start it.
As you play through the tasks, the chapter’s progress bar climbs up as well. Once you’ve completed the last task, not only do you advance to the next chapter, but you also get a special chest as a reward! The chest you will receive is shown at the top of the progress bar.