How do we put an iphone 5 sim card to iphone 4?

So first i got an iphone 4 my mom she open the line of number then she got a iphone 5 then she want to trade me my iphone 4 cause she said iphone 5 easy to lost the batteries and to light and to long. But my iphone 4 doesn't have a sim and the iphone 5 does so how to put the iphone 5 sim card into iphone 4, i know it smaller… And btw the company that we using is at&t

The 5 uses nanoSIMs & the 4 uses microSIMs. There are microSIM adapters where you could stick the nanoSIM in it & it'll have the size of a microSIM to use in a microSIM phone.