How did Mary Montagu discover a vaccine for smallpox

Lady Mary Wortley Montagu adapted "variolation" instead of "vaccination" to prevent smallpox in her children. She learned about it when she was in Constantinople (Turkey) with her husband. There, prisoners were intentionally inoculated with smallpox virus under their skin. When she saw that they didn't develop the disease and were among survivors, she inoculated smallpox virus to her children (son and daughter) as well using a needle. Later on, efforts of Edward Jenner towards vaccination were also recognized and it became a fashion to inoculate smallpox as a preventive measure.