The classical coup follows a pattern that has not changed since Julius Caesar crossed the Rubicon (spoiler: it was not a vacation). Step one: identify the key points of control in the capital. Step two: seize them simultaneously. Step three: tell everyone else what happened after it is too late for them to do anything about it (the definition of a fait accompli).
The most textbook example of the 20th century is Chile, 1973. Salvador Allende was elected president, which the United States did not like because he was a socialist and the US had a policy at the time that any socialist in the Western Hemisphere must be removed immediately (they called it the Cold War, I call it a tantrum with nukes). So the CIA spent three years destabilizing the economy, funding strikes, and building relationships with military officers. When the time came, General Augusto Pinochet struck.
The plan was simple: seize the naval fleet in Valparaiso, occupy Santiago with the army, arrest Allende, and announce that the military had saved the country from communism. Allende died in the palace (official story: suicide, disputed). Pinochet ruled for 17 years. Thousands were tortured. Hundreds were killed. The United States supported him the entire time (surprise).
The lesson of Chile: a coup does not need popular support. It needs speed, coordination, and the tacit backing of a major power. Pinochet had all three. Allende had the law on his side. The law does not stop bullets (a lesson worth remembering).
Coming soon: The Modern Coup, How to Overthrow a Government Without Tanks