To set up and use the breakout rooms feature in Daily Prebuilt, developers need to create a Daily room with breakout rooms enabled, join it as an owner, and then click on the "Breakout" button to start a session. The host can manage the sessions by dragging and dropping participants between rooms, sending session-wide chat messages, and ending the session when ready. Breakout rooms allow users to split off into smaller groups for more focused discussion, making them suitable for use cases like webinars, events, and large calls.