Changing physical SIM cards on your phone is always a fiddly business. First, you have to root for the little SIM tray tool that Apple includes in the box with its new iPhones – except those in the US ...
To remove the SIM card from your iPhone, you'll need to eject the SIM card tray with a special tool or paperclip.
The iPhone Air will only have an eSim - will other phone makers also shift away from the familiar - but fiddly - plastic ...