just pop in the sim after you switch out the old phone meid/esn number should do it.
I would call to make sure the swap went ok.
Also be careful that your unlimited is not cancelled. You are not subsidizing the phone so no loss of unlimited and no upgrade fee is required. Also make sure the phone is cdma and not gsm. Verizon uses cdma.
Better yet go into the verizon corporate store.
The OP will need a new SIM card. The card is the 4S is a micro SIM and is for overseas use only. The iPhone 5 uses a 4G LTE nano SIM card.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
So all I have to do is activate the phone and go to the Verizon store and buy a new 4G LTE nano sim card?
SIM cards are free at Corporate Verizon stores.