Current studies have indicated that whales do not have any form of language. Instead, think of how other animals, like dogs for example, communicate. Dogs use growls and barks to communicate a variety of things. Whales also use a variety of sounds to communicate. Studies show that whales might be communicating who they are, where they are or perhaps be some sort of pod identification.
Whales also use body language to communicate.
They use an underwater microphone called a hydrophone. A hyrdophone is designed to pick up sounds underwater just like a microphone is designed to pick up sounds in the air. Whale vocalizations are recorded. Then scientists use special equipment to study these sounds. It is a fascinating field.