How do I set up file syncing between my phone and computer?

For local syncing without the cloud, the most reliable option is Syncthing. It's a free program that works on a direct peer-to-peer exchange principle between devices on the same network (or even over the internet if needed). You install it on your computer and phone, specify the folders you want to sync, and then everything happens automatically. No cloud servers involved - just your devices talking to each other directly.

An alternative is Resilio Sync, which also works on a peer-to-peer basis, but some of its features are paid. If you're on Windows and have other Apple devices, you can use built-in solutions like OneDrive or iCloud, though they still go through the cloud. But if you want maximum simplicity and are okay with using the cloud in general - Google Drive and Dropbox, you just install them on both devices, specify a folder for syncing, and you're done.

If your Wi-Fi is unstable or you're on the move a lot, the cloud is still more convenient. But if your devices are at home on the same network, Syncthing will definitely solve your problem.

If you want a local solution without the cloud, try Syncthing - it's a free program that syncs folders between devices on the same network, and it works reliably. For Apple there's built-in syncing over Wi-Fi if you connect your phone to your PC. Another option is just to plug your phone in via USB and set up auto-sync in Windows Explorer, though that's less convenient than Syncthing. What OS are you running on your computer, by the way?