How does authentication work differently between asymmetric and symmetric cryptography? Must Bob and Alice establish a 'connection' before a symmetric or asymmetric encryption scheme is secure? If so, is there ever some expected plaintext whose decryption authenticates the users?

In addition, could anyone recommend a good introductory book or paper on cryptography for a beginner like me?   Thank you very much.
A start would be the Wikipedia article about Authenticated Encryption, and the GCM mode is an AE-mode for block ciphers.  

Additionally to the key, IV and cypher text you need the authentication tag, which is generated during the encryption process.

Decryption reconstructs the tag and compares it two the original. If they do not match, the decrypted text is invalid.