How to change the service of an iPhone?

My friend is giving me his iPhone 4S but he has AT&T and I have Verizon I know you have to change the SIM card but what if his service is still working? Does he have to call and tell them he no longer has the iPhone or can I just somehow change the service over to verizon my self? I'm new at all this technical stuff. I want to move a iPhone over from AT&T to Verizon even if the cell phone is still in use? Can I do that? Please respond!

Added (1). I would be using the Verizon 4G SIM card for the iPhone

Not going to work. The AT&T iPhone is not compatible with the Verizon network.

I don' think so.AT&T is a GSM carrier whereas Verizon is a CDMA carrier and technologically both are very different from each other. As you said you have Verizon and apple iphone comes in two models. One GSM and other CDMA. GSM one uses a SIM card whereas CDMA doesn't uses any SIM card (Except some models where there's a GSM SIM slot to provide international roaming).In simple language there's NO SLOT TO INSERT A CDMA RUIM CARD IN APPLE IPHONE.