Don't attempt to remove the SIM card while the device is powered on. Doing so may harm the SIM card and/or the device.
Verizon supports the Microsoft Surface 3 on Windows 8.1 Pro OS. Contact Microsoft Support to assist with any Windows 10 Pro OS How to and troubleshooting questions.
If your device is not running Windows 10, refer to Windows 8 for further instruction.
Ensure the device is powered off.
From the bottom edge of the device, remove the card tray.
Utilize the insertion/removal tool (it comes in the box with the device) to unlock the tray by inserting it into the provided slot then remove the tray.