On the bottom end of the remote you will see a small circular depression. If you press this with a tool (like the end of a ball-point pen) it will release a tray from the bottom of the remote. Pull the tray fully out of the remote and you'll see two coin-cell batteries. Replace them per the orientation indicated on the tray, then push the tray back into the remote until you feel it latch securely.
Please note: If you have the SHIELD Remote (2015) with rechargable battery, you can recharge it by:
1) Connect microUSB cable such as the one that came with your NVIDIA SHIELD to the microUSB port on the bottom of the SHIELD Remote.
2) Connect the other end of the USB cable to a USB charger or to an available USB port on the NVIDIA SHIELD.