A Lesson in Future History
The first stage of the classic plot analysis is all about exposition—i.e. the stuff you need to know to figure out what's going on. During this stage, we learn who the characters are, the kind of world they live in, and the conflict that will lead to the other four stages of the plot.
In The Moon is a Harsh Mistress, we learn about Mannie and his relationship with Mike, the self-aware computer. When Mannie goes to the Sons of Revolution rally, he (and we) learns about some of the problems facing the Loonies under the rules and laws of the Lunar Authority. After the Warden's bodyguards crash that party, Mannie meets up with Wyoh and Prof, introducing us to the rest of the main characters. When Wyoh, Prof, Mike, and Mannie join forces, we move from the exposition to the rising action
During the rising action stage, a series of events circle around the conflict between the Loonies and the Lunar Authority, leading up to the point of no return. Mannie and his group of co-conspirators begin planning the Luna revolution and eventually overthrow the Warden and the Security Chief. Despite winning the revolt, though, Mannie and Prof must head to Earth to convince the Federated Nations to recognize their claim to legitimacy. Failing, Mannie and Prof must then escape from Earth and return to Luna with all-out war a guarantee. Wee.
Moon of Warcraft
Welcome to the point of no return—and just like it sounds, from here, there is now no turning back for Mannie and company. When the Federated Nations assault Luna with their troops, the Loonies fight back, managing to defeat the invading forces. But the victory means the Federated Nations will continue to attack, and next time they might just bring the big guns—and by big guns, we mean nuclear weapons. Gulp.
It's Basically Life-sized Missile Command
The falling action plays out the conflict between the Loonies, especially Mannie, and the Federated Nations. Mannie begins bombarding Earth with moon rocks, and the Federated Nations send ships to destroy the catapult. Although they succeed in destroying it, they miss the secret catapult, Little David's Sling. In an intense standoff, Mannie bombards Earth while keeping the catapult's location hidden from the attacking ships. The Federated Nations accept the Luna Free State just before Mannie runs out of ammunition for the catapult. Phew.
Moving on Up
Now we get the denoument, or resolution. With the Luna Free State established, it's time for the story to begin tying up loose plot ends. Prof dies while delivering a speech to inaugurate the new state, and Mike is lost after the enemy attack jars his system. Mannie and Wyoh stick around politics long enough to establish the official Luna flag, but Mannie has thoughts of heading out to the new frontier of the asteroids and seeing what he finds out there.