DIAGNOSIS It's rarely your apps or photos. The main culprit is cached data from streaming apps and, more importantly, temporary system files and software update downloads that didn't clean up after themselves.
FIX Start by clearing app caches. Go to Settings > General > Manage Storage. You'll see a list of apps. Select the biggest ones (usually streaming apps). Inside each app's storage menu, you often have the option to 'Delete' the app (which removes its data) or 'Offload' it. Offloading keeps your login but deletes the cache. Do this for a few large apps, then reinstall them from the App Store if needed.
IF THAT DIDN'T WORK You need to clear the system's temporary update files. The only surefire way is to do a full reset, but you can keep your settings. Go to Settings > System > Reset. Choose 'Reset All Settings.' This will not delete your apps or accounts, but it will clear system caches, network settings, and preferences, which often frees up several gigabytes.
HEADS UP If you frequently see this warning on a 64GB model, consider the 128GB version next time. The OS and its overhead take up more space than you think. Also, avoid using the Apple TV as a HomeKit hub for a ton of security cameras, as video thumbnails can eat storage.