While her story is legendary, we know very little about her life before the war. She was most likely born into a poor family and didn't have access to the kind of education that was common for wealthier women at the time.
It's important to note that the "Molly Pitcher" story, while rooted in reality, has been romanticized and exaggerated over time. It's likely that she did help out her husband, a soldier, during the war by carrying water to the troops, and she might have even taken over his cannon when he was wounded.
So, while we can't say for sure what kind of education she had, it's safe to assume that she was largely self-taught and learned through experience.