The term "ballad" has two distinct meanings. It can refer to a narrative folk poem, usually told in short stanzas that are often sung. It can also mean a sentimental or romantic song. Either way, the theme of a ballad will refer to the message presented by the author of the piece.
The Big Idea
To figure out the theme of a ballad you must first ask yourself what the author's big idea was. What message was he trying to convey to you, the reader or listener? These lessons are usually about how to live a better life, the nature of the universe or common human concerns like good vs. evil.
Not the Topic
Be aware that the theme is not the same thing as the topic. A folk ballad might be about a railroad worker, a cowboy or an apple tree farmer, and still have similar themes. Romantic ballads may all be about love, but have wildly different messages to tell. The message, not the topic, is the key element.
Read Between the Lines
The theme of a ballad will not usually be stated directly by the author. It takes inference on the part of the reader. Think about the characters' actions and words. Think about the events and situations in the song or poem. Then determine what the author is saying about the topic.
The Author's Opinion
Themes are based on the author's opinions and ideals. You may not agree with his message, but should remember that it's not your place to modify that message to suit your ideas. Do not infer so much that you, the reader, take over for the author.
When you believe you have found the themes of the ballad, it's critical you have textual evidence to support your ideas. You must be able to explain how the themes are presented in the ballad. Like detective work, theme discovery is a partially creative process, but must have support.
Most ballads will have more than one theme or message intended by the author. Because finding themes depends upon your own inference as well, you may find unintended themes as well. If you can support these themes, they may be valid.