SHIELD TV supports microSD cards - UHS Class 1 or faster.
SHIELD TV Pro supports external USB flash drives and hard drives. To maximize speed and performance, NVIDIA recommends USB 3.0 flash drives.
To expand your internal storage for apps and games, your USB or MicroSD drive will need to be set up as internal storage. Go to Settings -> Device preferences -> Storage -> Select the drive name, then select the "Set up as internal storage".
If you have a Network Addressable Storage (NAS) you can connect your SHIELD TV over the network to access your shared content.