If you have the cellular version of the watch, you need to contact your carrier and have them start service on the phone. This will have a monthly fee just like your phone.
If you have the Bluetooth version of the watch, the watch does not connect to your cellular plan. It only connects to your phone via Bluetooth.
I just had this problem with mine last week. I was about to send mine back and get a new one also. After 2 days of calling Verizon and Samsung I did some research of my own and found out that if they take your old watch line off your plan completely and add a new one for the new watch it fixes the problem. Mine worked right after they did that. Good Luck