The most readily available information on the success rates of any fertility clinic is probably the overall success rates for any given procedure. That refers to live births after invitro fertilization, for instance, or live births after IUI. This information is available directly from the fertility clinics you are considering for treatment, either through an appointment at the clinic itself, and very often also on their website.
But perhaps a more reliable source of information about fertility clinic success rates in the United States is the website of the Centers for Disease Control and Prevention, or CDC. In their section about Assisted Reproductive Technology (ART), you can find comprehensive information about the success rates of all fertility clinics in the US. When you are going through this information, remember to research more than the clinic's overall success rates. Knowing what the success rate is for the exact procedure you will need, for your age group, is the most relevant. How you choose a fertility clinic ultimately depends on a bit more than the success rate alone. But it is certainly a very important factor, about which you want as much information as possible. If you're in the United Kingdom, we've also got some information on fertility clinic success rates in the UK.