Cryptography ensures that transaction amounts, sender, receiver are encrypted. There is no way to decrypt the data. You can verify the encrypted data without decrypting it. Everything works similar to Bitcoin but now you and others have no way of figuring out anything valuable by looking at the blockchain, because everything on the blockchain is just encrypted bytes.
Even the node that is the first one to receive all bytes has no idea who is sending, receiving and the amount. Everything is always encrypted.
When I create a transaction that includes my wallet address and the address that receiver gave me, once the transaction is made, the receiver cannot see the original address of my wallet, the 3rd party cannot see the amounts or addresses in the transaction and the receiver can move the money to a different address and I would have no way of figuring out that happened. Similarly, receiver can send me back the amount and I would have no idea from which wallet address it came.
Generally what happens is that: - Everyone is able to prove a transaction's correctness; - There's no way for a third party to track the contents of a transaction adversarialy; - there are ways for first and second parties to prove them if they so wish.