Q: My phone keeps saying invalid SIM and doesn't work.  How do I fix this? I didn't even know iphones had SIM cards

Where are you located? Did you purchase your iPhone new? Who is your carrier? These answers need to be in place to try and help you understand your device and the use of a SIM card.

Could be a bad SIM card or an iPhone hardware problem.

Try a new SIM card first. You can get a new SIM card at an ATT retail store. After explaining the problem, there should be no charge for the new SIM card.

If no change after that, call AppleCare or make an appointment at an Apple Store if there is one nearby.

I concur with what Allan had to say. On a side note, AT&T is a GSM carrier, and all GSM carriers use SIM cards. This contains subscriber information to use the device on the carrier.