To claim compensation for a JetBlue flight delay, check the airline's official policy on their website, ensuring your delay meets their criteria. Retain important documents like boarding passes, then contact JetBlue's customer service through their website, app, or by phone, explaining the situation and inquiring about compensation. Follow any provided guidelines for submitting a complaint or claim, including necessary details and supporting documents. Be patient during the process, and follow up as needed to check the status of your claim.