Don't attempt to insert the SIM card while the device is powered on. Doing so may harm the SIM card and/or the device.
Ensure that the device is powered off.
From the top edge of the device (display facing up), remove the card tray.
Utilize the insertion/removal tool (or a paperclip) to unlock the tray by inserting it into the provided slot (figure 1) then remove the tray (figure 2).
Insert the SIM card into the tray as shown (gold contacts facing down).
Ensure the card fits into place.
Insert the card tray (gold contacts facing down).
Press in on the tray to lock it into place.
Check out these interactive demos (S9 or S9+) for more info.