With perfect use, NuvaRing is between 98% and 99% effective. This means that among women who used it perfectly every time, 1-2 out of every 100 will get pregnant anyway within one year. This is the best accuracy of any contraceptive product, which is why people often combine multiple birth control methods.
Nuvaring works by altering your uterus's mucus membranes. Not sure it's 100% effective the first month you use it. Also, it's not effective during your cycle.