Diffie-Hellman is a key agreement protocol. It is used to establish a secret value (master secret) which is identical at the parties involved in the key agreement.
This value is then put through a Key Derivation Function (KDF) to derive one or more symmetric keys, such as AES keys, that are also identical for the parties involved. These keys can then be used to encrypt messages and to protect the integrity and authenticity of the messages between the parties. Sometimes the value is truncated or put through a one way function such as a hash function instead of using a well defined KDF.
The actual symmetric cipher, mode of operation and method of generating the authentication tag are not part of the key agreement protocol; basically they can be anything at all.
It is impossible for other parties to retrieve the secret value that has been agreed upon.
Then again, it is important to note that Diffie-Hellman does not authenticate the parties themselves. This should be performed as part of the protocol using different primitives such as signature generation functions. It's important that the public values used for the key agreement are also verified at some point in the protocol.