Empathy is often treated as a fixed trait, something a person either has or lacks, but most researchers who study it now treat it as a skill that responds to deliberate practice, much like a muscle that strengthens with consistent, specific use rather than remaining static throughout a person's life.
Practical exercises tend to focus on perspective-taking: deliberately pausing to consider a situation from another person's specific circumstances before responding, rather than reacting from one's own immediate assumptions. This small pause, repeated often enough, appears to genuinely change how automatically a person considers another viewpoint over time.
Active listening plays a similar role, since fully attending to what someone is saying, without mentally composing a reply while they are still speaking, forces a kind of attention that tends to build empathy simply as a side effect of the practice, whether or not that was ever the original intention behind it.