I got my first "baby" at the North Shore Animal League 8 years ago. My husband and I went and took a long time looking around. The staff was wonderful - they answered all of our questions and based on our lifestyle (whether we lived in a house or apt, were we gone alot of the day, etc), guided us to what type of dog would be appropriate for us. We finally found her - she was 9 weeks old at the time. The adoption process was pretty painless. They were thorough in checking our references - they only want their animals to go to good homes, so it's understandable to check references. When all was said & done, a few hours later, we went home with our new baby. They gave us all of her papers, medical information, etc - made sure we had everything we needed.
I highly recommend the North Shore Animal League to anyone who's looking to get a cat/dog in the NY Tri State area.