When do you use zoos or zoo's or zoos'?

Both are correct in the right context:

.

Zoo's is the possessive form of the singular noun zoo.

Example: The zoo's head keeper has resigned

Zoos is the plural form of zoo. eg We have three zoos in our city.

Zoos' is the possessive form of the plural noun zoos

Example: All of the zoos' keepers meet every month.