Then in the 300s BC, Greece was conquered by Philip of Macedon, and all of Greece began to be ruled by him as their king (in theory he was only leading a league of Greek city-states, the first among equals, but really he acted like a king). Athens and other Greek city-states still kept their local democracies or oligarchies for local government, but bigger decisions were made by Philip, and then by Philip's son Alexander the Great.
After Alexander died in 323 BC, Greece became a kingdom ruled by a series of Macedonian kings. The Macedonian kings let each city-state rule itself, so long as they paid taxes to the kings in Macedon, and sent soldiers to fight in the endless civil wars between rival Macedonian kings.
But then the Roman Empire gradually took over Greece (and Macedon) between 200 and 146 BC. From 146 BC on, Greece was a province of the Roman Empire, and ruled by far-off emperors. Even after the Roman Empire in the West collapsed, Greece was still part of the Eastern Empire. In the 1100s and 1200s AD, parts of Greece were taken over by Normans, who built castles and ruled as kings.
Learn by doing: design your own perfect system of government
More about the Greek court system
Oxford First Ancient History, by Roy Burrell and Peter Connolly (1997). Lively interviews and pictures make the ancient Mediterranean come to life. For teens.
Cleisthenes: Founder of Athenian Democracy, by Sarah Parton (2002). A biography of the founder of Athenian democracy.
Athenian Democracy, by A.H.M. Jones (reprinted 1986). One of the great social historians of the 20th century, though this isn't easy going.
Alternatives to Athens: Varieties of Political Organization and Community in Ancient Greece, a collection of essays edited by Roger Brock and Stephen Hodkinson (2003). Each chapter presents a different kind of Greek government: oligarchies, tyrannies, monarchies, and so on. By specialists, for specialists.
Rome, the Greek World, and the East: Government, Society, and Culture in the Roman Empire, by Fergus Millar, Hannah M. Cotton, and Guy Rogers (2004). Millar is an expert on Roman government. This book deals with how the Romans governed in Greece.
Centuries, by Lord Kinross (1979). A short introduction to Ottoman
government, for the non-specialist. It's a little out of date, so it
doesn't consider the role of Islam, or the role of women, as much as
it might have.