Formal:
* Uspokój się. (Literally: Calm yourself.) This is the most direct and formal translation.
* Zachowaj spokój. (Literally: Maintain calm.) This is a more polite and indirect way to say it.
Informal:
* Uspokój się, kochanie! (Calm down, darling!) This is a more casual and affectionate way to say it.
* Spokojnie! (Calmly!) This is a short and informal way to say it, similar to "Chill out!" in English.
* Odetchnij głęboko. (Take a deep breath.) This is a suggestion to help someone calm down.
Other options:
* Nie denerwuj się. (Don't get upset.)
* Nie panikuj. (Don't panic.)
The best phrase to use will depend on the situation and your relationship with the person you are speaking to.