To understand their language we need shared experiences, shared emotions, common internal worlds. Observation of dolphin-dolphin interaction would help but to a limited degree.
It would help if the dolphins are also interested in teaching us. Dolphins or we could say to the other '... that is how we pronounce sea-cucumber'. Shared nouns would be the easiest.
The next level, a far harder level, would be to reach the stage where we can say 'the emotion that you are feeling now, that we call "anger"'.
We will no quite have the right word for "anxiety that I feel when my baby's blood flow doesn't sound right in Doppler".
Teaching or learning 'ennui' and 'schadenfreude' would be a whole lot harder.
This begs a question can one fully feel and understand an emotion we do not have a word for ? Perhaps Wittgenstein has an answer.
Postscript: I seem to have triggered quite a few of you and that has me surprised. I thought this would be neither controversial nor unpopular. It's ironic in a way. If we can't understand each other, understanding dolphin "speech" would be a tough hill to climb.