By popular votes of all those that were qualified citizens (To be a citizen you must be 18 or older, A male, Own property and Be born in Athens, the home of democracy) along with an assembly (Gave an opportunity for men to vote on laws and debate.) Also, Democracy was limited because 1. not all Greek city-states were democratic for example, Sparta. B. Not everyone could vote. (especially women.)
Sorry this might not be a short essay but I hope this helped.