We cannot decrypt a cipher text without a key. Hashing is an irreversible process. It wont work in your scenario. There are two types of cryptography techniques: Symmetric and Asymmetric.
Asymmetric cryptography is maintaining two keys for everyone:public key and private key.When you want to communicate with someone, you should encrypt the plain text using their public key and they will decrypt the same using their private key. When they want to communicate with you, they will encrypt the plain text using your public key and you can decrypt the same using your private key. So every party should hold two types of keys.
Symmetric Cryptography is maintaining a single key for a communication. The single key will encrypt and decrypt the data. When two parties wants to communicate, they should have a shared secret key (common key). When you want to communicate, you can encrypt the plain text using the key and they will convert back the cipher into plain text using the same key.
In your scenario, you can use Symmetric cryptography techniques such as AES,DES etc., You can maintain a separate key for every user. You can use that key for encryption and decryption. The keys can be stored in another database. whenever you want to display the password in plain text, you can take the key for the user and decrypt it using the same cryptographic technique.