The useful first step at John F. Kennedy International Airport is to treat the airport's own transportation page as the source of truth. After baggage claim, follow current rental-car signs and keep the destination---AirTrain to Federal Circle---in view rather than navigating to an unrelated public address.
For JFK, follow airport signs to the AirTrain and verify the current Federal Circle connection before choosing a rental counter. Construction, terminal changes, and operating notices can affect the best transfer path, so use JFK's current guidance on the day of travel.
Before leaving the facility, confirm the agency's current hours, identification and payment requirements, vehicle notes, and return instructions. Photograph the vehicle condition and keep the official airport and agency pages available for the trip home.