How do I obtain a Nano-sim card for my phone?

So, I have my Galaxy phone under contract but I do not like it and I wan to sell it. Hence I ordered a phone-out-of-contract that I like. My plan was to switch the sim card into it and enjoy! However, the new phone has a tinier… a “nano-sim card” that I got along with it where as my old Galaxy has a bigger sim card.

How can I get this fixed? Will At&t help program the new sim card for me?