I tried to search on the Black Widow page on how she escaped from the Red Room and how she freed herself of the subjugation mind control but I couldn't find anything. Was it ever explained? Because I remember yes.
She was on a mission and encountered Hawkeye, who went to kill her. He decided to bring her back to SHIELD. As for the mind control, it was retconned, so there isn’t an explanation for that as of now
Pretty sure the literal mind control was a more recent development whereas before, as others have said, the Red Room relied on more "traditional" indoctrination methods