First, do a quick review of when to use ser and estar for describing people. Ser usually applies to inherent qualities, such as physical characteristics or other aspects that are considered permanent. For example, a singer es cantante, a tall person es alta (or alto). Ser is also the appropriate verb when describing nationality and skin color. (El es mexicano. Ella es morena.) Estar, on the other hand, usually refers to physical location (el está en la escuela), temporary conditions (ella está enferma) and describes actions in progress (ellos están caminando).
Next, break your class up into groups of two or three. Each group should brainstorm four or five well-known celebrities, then write descriptive sentences about those celebrities, using ser and estar as appropriate. For beginning groups, provide photos for them to choose from and use as an aid for creating descriptive sentences, and a vocabulary cheat sheet if necessary. More advanced groups can do this activity without the photo or vocabulary prompts. By the time the brainstorming period is over, each group should have at least three ser sentences and three estar sentences to describe each celebrity. Have them keep as quiet as possible during the brainstorming process, so each group is unaware of the other groups' celebrities.
Call on each group in turn to read out their descriptive sentences for the celebrity of their choice, all in Spanish, of course. For example, if a group is describing a famous athlete whose team just lost a big game, they could use sentences like está deprimido, or está molesto con su entrenador. Write the sentences on the board, or have one of the group members come up and do so. For a beginner-level class, you can also hang all the celebrity photos on the board as visual prompts; assigning several celebrities to more than one group helps ensure that your students won't get the last few by simple process of elimination.
Once all the sentences have been read and written, let the class guess until they come up with the right identity. Rotate throughout the class, giving each group a chance to read off descriptors for at least two celebrities. Depending on how the class responds, you might keep going through them all.