From the FDA approved patient leaflet:
Insert NuvaRing on the first day of your cycle, (i.e., the first day of menstrual bleeding). NuvaRing will work immediately, it is not necessary to use an additional contraceptive method. You may also start on Day 2 to 5 of your cycle, but in this case make sure you use an extra method of birth control (barrier method), such as male condoms or spermicide for the first seven days of NuvaRing use in the first cycle.