How to transfer an iPhone 4 SIM Card?

So I just got my second iPhone 4 for free because of a sleep/wake button defect, Verizon sent me a brand new iPhone 4 in the mail. It came with an instruction sheet that is telling me to remove the phone's SIM card in order to transfer all my contacts and all that. I looked up some Youtube videos on how to remove it but they were all iPhone 4s' and they had the little dot on the side to remove it with a paperclip. My iPhone 4 has nothing on any sides, just the buttons, the headphones slot, and the mic. The mic hole kind of looks like the hole for the paperclip but I don't see any slots for the card to even come out.

You would take the SIM card out of the other phone and simply put it in the other. On my 4 you would put a needle in it and it would pop right out.