How does the doctor know if the diagnosis is puncture wound of the knee?

History & physical: Usually by performing a history and physical examination with possible radiologic evaluation.

Depends: A puncture wound of the knee (skin) is less serious than a puncture wound into the knee joint, itself). If the foreign object went into the knee joint, it might carry germs into the joint which can be more serious than if it punctured the skin but not the joint capsule. Sometimes an x-ray can tell the difference, sometimes not. Washing out the wound and a tetanus shot are key, either way.

By history: Its hard to know what you are asking based on how you've phrased it. A puncture wound should be obvious by history. The doctor will see it and treat it accordingly.