Component testing with Vue Test Utils involves mounting a Vue component in a test environment, simulating user interactions such as clicking a button, and then checking if the component updates its display or state correctly. The process starts by importing the mount function and the component to test. Mounting creates a live instance of the component. Then, we find elements inside the component and trigger events on them. After the event, the component updates its internal state and re-renders. Finally, we assert that the output matches what we expect, confirming the component behaves correctly. This step-by-step approach helps catch bugs early and ensures the component works as intended.