I get No Service Message with SIM installed?

Unfortunately, this can mean a few things. But! Here are some suggestions and things to try to save the trip to your carrier or a whole loop of going back and forth.

1. Make sure the SIM Tray is properly seated and is fully slotted in. If there is resistance or it is not fully seated, there may be debris in the port.
2. Check inside the slot carefully, see if there is any debris lodged in there as it can be keeping the SIM from being recognized. Carefully remove debris.
3. Clean the SIM Card. First off, I would inspect it. Any noticeable discoloration or damage would indicate that you will need a new SIM, but a small smudge or a piece of debris can be removed! Taking a soft, non abrasive cloth and cleaning the SIM gently.
4. Update the iPhone to latest iOS Release. Sometimes all you need is an update to correct any faults.

Hope this helped! Good Luck!