For those who know it may be obvious but their are plenty of people that could miss that micro hole on the side as with other Smartphones they are labeled and not so well integrated into the design.
Here is a Full tutorial on how to open the tray on your iPhone, remove and insert nano sim into the sim card slot.
Locate the Sim card try (little hole on the right side)
Find the sim card removal tool within the box of your iPhone. Or you can use something like a paperclip or an earring wire.
Insert the removal tool into the hole, press hard and tray should pop out.
Remove or put in the Sim card into the tray carefully, flat and flush.
Insert the tray back into the phone and press to close the tray.
Here is a video for a closer look: