For a three-act plot analysis, put on your screenwriter’s hat. Moviemakers know the formula well: at the end of Act One, the main character is drawn in completely to a conflict. During Act Two, she is farthest away from her goals. At the end of Act Three, the story is resolved.
Act I
The first third of Paine's pamphlet introduces the argument for American independence and focuses on the contradictions and corruption that are built into the English Constitution. Paine finds it insane that the constitution would give divine power to a king and then give a group of elected officials (The Commons) the power to deny this king's wishes. He also has no time for aristocrats, who don't earn their positions of power but only inherit them on the basis of which families they're part of.
Act II
After thoroughly trashing the English political system and the idea of inherited power, Paine turns to a discussion of the current state of affairs in America. Things aren't exactly sunshine and rainbows and unicorns: the British have recently taken military action to show that they're willing to oppress Americans with violence in order to keep everyone in line.
There are a lot of people who think there's still time to patch things up with the ruling country, but Paine argues that the time for reconciliation is over. It's time for America to stand up and seize its independence. U.S.A! U.S.A! U.S.A!
Act III
The third part of Paine's argument mostly lays out all of the reasons why an American insurgence would be successful. For starters, Paine painstakingly lays out calculations for how much it would cost to build an American fleet of ships that could take on the British navy. Next, he shows why America's natural resources would provide Americans with everything they need to furnish supplies for a successful army. When he's done with this, he restates his case for why America needs to act sooner rather than later in fighting the British: time is of the dang essence, y'all.
In an Appendix published later than the rest of the pamphlet, Paine criticizes a few things that have been written since he first published. The first is a speech from the King of England threatening America with certain doom if they rebel. Paine uses this as another clear example of why America must throw off its oppressors. He also goes after a pacifist Quaker writer who has argued that Americans shouldn't get involved in armed conflict because God will sort everything out in the end. Paine is especially hard on this point of view, and he wraps up his arguments by calling on Americans to shun and insult anyone who preaches pacifist or Quaker ideas about the American Revolution.