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
Henry marries Margaret and is forced to give up some French lands for her. A bunch of the nobles complain about this and blame each other for causing the problem. Still, the real problem (according to the nobles) is Gloucester: he was appointed Protector way back when Henry was a baby and needed help ruling, but Henry doesn't need him now.
The nobles conspire against Gloucester. His wife makes it pretty easy for them when she gets a little too ambitious and dabbles in some good old-fashioned witchcraft. She's arrested, and Gloucester is shamed.
Act II
Gloucester is bummed about his wife's banishment, but he knows she was guilty of the crime. Suffolk, Margaret, and Beaufort try to think of some excuse to off Gloucester and then just decide to kill him without any pretext. Sure, they could await his trial, but they can't think of any charges that will stick. (We wonder why…)
Once Gloucester is murdered, Henry mourns for his friend. Meanwhile, York has been working behind the scenes on his own plan: he's hired Jack Cade to start a rebellion, and that's exactly what Cade does—with some pretty bloody and chaotic results.
Act III
The rebellion is in full swing, with nobles taken down left, right, and center. Cade promises there will be no more reading and writing. Power to the people? Well, it's all fun and games until Cade realizes that his army will follow anyone with a rousing speech. That freaks him out, so he flees... and is killed.
None of this seems to matter to York, who just picks up right where his comrade left off. He uses Henry's divided kingdom to his advantage by fighting Henry and (what's left of) Henry's men. Henry flees, afraid for his life. York wins the battle and hurries back to London to try to defeat Henry there, too. This time, it's for the crown.