When an investigator becomes delayed, he tips his investigator token on its side to remember that he is delayed.
A delayed investigator cannot perform any actions.
This is true even if he would be granted an additional action out of his turn, for example from Charlie Kane's ability.
Instead of performing actions during the Action Phase, a delayed investigator rights his Investigator token and is no longer delayed.
This is true even if the investigator cannot perform actions, such as while he has a Detained or Lost in Time and Space Condition.
If an investigator would become delayed on his turn during the Action Phase, he immediately ends his action and loses all remaining actions instead of becoming delayed.