...Athenian democracy (click here) was a direct democracy made up of three important institutions. The first was the ekklesia, or Assembly, the sovereign governing body of Athens. Any member of the demos--any one of those 40,000 adult male citizens--was welcome to attend the meetings of the ekklesia, which were held 40 times per year in a hillside auditorium west of the Acropolis called the Pnyx. (Only about 5,000 men attended each session of the Assembly; the rest were serving in the army or navy or working to support their families.) At the meetings, the ekklesia made decisions about war and foreign policy, wrote and revised laws and approved or condemned the conduct of public officials. (Ostracism, in which a citizen could be expelled from the Athenian city-state for 10 years, was among the powers of the ekklesia.) The group made decisions by simple majority vote....
Greek democracy was the purest form of practice, but, it was definitely racist. The only voting members of the ekklesia were men citizens. They each had a vote in government and it was counted.
The government decisions were by majority vote.
It was during the Hellenistic Age that democracy became more intense and practiced in city-states by the demos (the citizen body). As the Greek Empire grew it was better to allow the local authority to carry out governance. That meant that while it was all a democratic process, it varied from the governance of Athens.
But, remember the context of this "idea" of democracy. It was a group of individuals that found the need to define governance. Right? This was 800 years before the change in the timeline of history from BCE to CE. That is a long time for an idea to take a concept and provide governance. In a civilized society, it almost seems like a natural order, in retrospect.