How to use my iPhone 4S in London & Paris?

Next week, I'm going to London for 2 days and Paris for 6. I have Verizon and was told by them about their data plans, but now I'm being told they are scams, and I really don't want to come back to the US To a $500 cell phone bill.
I was told of some ways to unlock my phone and then get a SIM card, but I'm not sure of the steps I need to take?
I will only be making very short phone calls to my cousin there when I meet up with her and then need to use data for apps, maps, and such.

Any advice on the correct steps to take for this without spending a ridiculous amount of money would be very helpful!

Your IPhone should have a sim card in it. Have Verizon unlock it. There's no scam, but using an American phone in Europe isn't cheap! That's all there's to it.

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