I live in NY and served my tenant a 30 day notice to vacate and she hasn' t moved. What do I do next?

You go to your local housing court and file for an eviction order. The county courthouse can tell you where to go

I will add, if you are a landlord, you should know the laws about payments, evictions, violations of lease agreement before you rent. Now would be a good time to hire an attorney by the hire to review your obligations and rights.

Also as a landlord it is good to have preprinted forms for almost any possible occasion.

Did she have a lease, was it up?

You're going to have to file a lawsuit for eviction. The forms should be available in the court clerk's office but they probably won't be very helpful when it comes to filling them out. I suggest that you get an attorney to handle it this one time. Call the court clerk, ask which day they'll be hearing landlord/tenant cases, go to the courthouse and watch. You'll see attorneys who have anywhere from 5 to 30 cases. Speak to them afterward and see if they'll take your case for a set fee, such as $200 or so. It's possible that you'll be able to charge the tenant for the legal fee.

Waiting to hear your answer to my question, why were giving her notice? If she was on a lease was it up or was there a violation of terms?