Using encryption. When you take a picture, the device or app creates a signature using the photo data and metadata.
Then you can check the signature using the company’s public keys.
If you make edits to it, the editing app will package the new metadata, edited photo data, the original signature, and sign it again.
Now you have a chain of “changes” and can inspect and validate its history. It works for video and audio too.
As long as the private keys aren’t leaked, there’ll be no way to fabricate the signatures.