The Basis of Lightning Technology is a standardized technical specification for the implementation of the Lightning Network. The standards define how various implementations can interoperate to interact with and create the same network. The specifications are currently a work-in-progress, and are continually being iterated upon as projects like lnd and c-lightning are built in parallel.
The Basis of Lightning Technology (BOLT) documents describe a layer-2 protocol for off-chain bitcoin transfer by mutual cooperation, relying on on-chain transactions for enforcement if necessary.
See BOLT #2: Channel Establishment for more on channel establishment and BOLT #3: Funding Transaction Output for the format of the bitcoin transaction that creates the channel. See BOLT #5: Recommendations for On-chain Transaction Handling for the requirements when participants disagree or fail, and the cross-signed bitcoin transaction must be spent.
See BOLT #7: P2P Node and Channel Discovery for details on the communication protocol, and BOLT #10: DNS Bootstrap and Assisted Node Location for initial network bootstrap.
See BOLT #11: Invoice Protocol for Lightning Payments for the protocol describing the destination and purpose of a payment such that the payer can later prove successful payment.