Principle? First of all, public key system, you know? Only the public key can decrypt the content encrypted with the private key.

Then digital signature is to hash the content that needs to be signed (generally SHA algorithm) and then encrypt it with private key to get digital signature.

Verifying signature is to hash the content and compare it with the decryption result of additional digital signature with public key. If they are consistent, it means that the content has not been tampered with.