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. Using two new CR2032 batteries, replace them per the orientation indicated on the tray, then push the tray back into the remote until you feel it latch securely.
Video Demonstration of replacing batteries in SHIELD Remote 2017
If you have the SHIELD Remote with a headphone jack, it has a USB-rechargable battery.
To charge:
1) Connect a 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.
Please note: This article is for the SHIELD TV Remote (2017). For instructions on how to change the bateries on the SHIELD TV Remote (2019), please use the following FAQ: How to open the NVIDIA SHIELD Remote (2019) battery compartment