At the time of the Ark's descent, it is believed that most Grounders speak only Trigedasleng; warriors (and certain other Grounders) speak both Trigedasleng and Modern English, a fact which they are careful to hide from their enemies.

Do grounders speak?

In the show "The 100", the Grounders speak a language called "Trigedasleng". This language is intended to be a descendant of modern English, and we are to understand that it arose through natural linguistic drift.

Can you learn Trigedasleng?

During the hundred years since the bombs, the code was adopted into their everyday language, ending up with "modern day" Trigedasleng. The language is fun and easy to learn (especially for native English speakers).