http://www.historyforkids.org/learn/greeks/government/athens.htm

Aristotle divided Greek governments into monarchies, oligarchies, tyrannies and democracies, and most historians still use these same divisions. For the most part, Greece began by having monarchies, then oligarchies, then tyrannies and then democracies, but at each period there were plenty of city-states using a different system, and there were many which never did become democracies or tyrannies at all.

In the Late Bronze Age (the Mycenean period), between about 2000 and 1200 BC, all Greek city-states seem to have been monarchies, ruled by kings. Homer's Iliad, and Greek mythology in general, shows us a whole series of kings like Agamemnon and Theseus, and some of their palaces have survived for archaeologists to dig up.

After the Dark Age, though, only a few Greek city-states still had kings. Sparta is the most famous of these, though actually Sparta had two kings, usually brothers or cousins, at the same time. One would stay home and the other go off to fight wars.
Most city-states in the Archaic period were ruled by oligarchies, which is a group of aristocrats (rich men) who tell everyone else what to do. Then in the 600's and 500's BC a lot of city-states were taken over by tyrants. Tyrants were usually one of the aristocrats who got power over the others by getting the support of the poor people. They ruled kind of like kings, but without any legal right to rule.

In 510 BC, the city-state of Athens created the first democratic government, and soon other Greek city-states imitated them. Even city-states that weren't Greek, like Carthage and Rome, experimented with giving the poor people more power at this time. But Athenian democracy did not really give power to everyone. Most of the people in Athens couldn't vote - no women, no slaves, no foreigners (even Greeks from other city-states), no children. And also, Athens at this time had an empire, ruling over many other Greek city-states, and none of those people living in

Athens was a town in central Greece, which was settled very early because it has a good seaport nearby (at Piraeus) and a steep hill which makes it easy to defend. Athens was already an important city in the Late Bronze Age, and appears in Homer's Iliad as the kingdom of Theseus. There was almost certainly a Mycenaean palace on the Acropolis, and lots of Mycenaean pottery has been found in Athens.
During the Dark Ages, Athens declined like other Greek towns, and the old palace was abandoned, but the Athenians were proud to say that unlike Sparta or Corinth, Athens had never been sacked by invaders.
In the early Archaic period, around 900 BC, Athens began to grow again. When we first see the Athenians after the Dark Age, they have an oligarchic government. A group of rich men (but not women) got together to make the laws and decide everything.

During the Archaic period, the system of government seems to have been pretty severe for ordinary people, and to have favored rich men and women. In 621 BC Draco was serving in the government of Athens as an archon. Draco was a rich man, part of the oligarchy. He ordered his slaves to write down the laws, so that everybody would know what the laws were and the rich men in the oligarchy wouldn't be able to just make up laws to suit themselves. These laws said that poor people could be killed for even small crimes like stealing a cabbage. The laws also had different punishments for poor people and for rich people. If a poor woman owed money to a rich man, she would be sold into slavery to pay the debt. But if a rich man owed money to a poor woman, his punishment was lighter.

But most people in Athens weren't happy when they saw the laws written down - they were angry! They thought these laws weren't fair. They complained especially about debt bondage - being sold into slavery because you owed somebody money. So in 594 BC the Athenian oligarchy chose another rich man, Solon, to fix the government. They told him, "Do something so everyone won't be so mad at us, but let us keep all the power." (We know about Draco and Solon mainly from the Greek historian Herodotus).

Solon changed the law so that poor people could not be sold into slavery just because they owed people money. He cancelled debts and redistributed land so people got a fresh start. He changed the law so that people couldn't be killed except for any crime except murder.
Under Solon's rules, the rich men in the oligarchy kept most of their land and most of their power. But he did start an Assembly, that any citizen could come to and vote on important questions. And he decided that judges would be chosen through a lottery, so that even poor men might be judges. He did not allow women to be in the Assembly or to be judges. He did make it illegal for parents to abuse their children. For a while, this worked. The ordinary people weren't so angry, and the rich men got to stay in power.