My new iPhone can't make calls, send texts, and has no service?

I just got a new iPhone 5S. I plugged it into iTunes to transfer my backup from my current iPhone 5. All my apps, songs, pictures, and email transferred. I can use my apps and get online. I just have no service and can't send texts or calls or anything. I can still call and text from my old phone.
How do I fix this?

Obviously you have to tell your carrier you switched phones, they don't just know by magic.

Remove the SIM card from the old iPhone 5, and insert it into the iPhone 5S. There's a tiny door that you can open up with a paper clip on the phone that contains this card, and it controls your phone service. You have to move the card to the new phone in order to have service transferred to the new phone.