To test an oil burner ignition transformer, first, ensure the power is disconnected for safety. Use a multimeter to check the primary voltage; it should read around 120 volts when the burner is activated. Next, measure the secondary voltage; the transformer should output approximately 10,000 to 15,000 volts. Inspect for any physical damage or burned connections and check the continuity of the primary and secondary windings. Ensure that the ignition electrode is correctly positioned and free of soot or debris. If the readings are outside the expected range or there is visible damage, consider replacing the transformer. Always follow manufacturer specifications and guidelines for accurate results.