Most good stories start with a fundamental list of ingredients: the initial situation, conflict, complication, climax, suspense, denouement, and conclusion. Great writers sometimes shake up the recipe and add some spice.
Exposition
The Bad Beginning
Henry V goes and dies, leaving the English aristocracy in an uproar. The next king is literally a baby, the French territory Henry conquered is rebelling, and the nobles may not be able to get along while waiting for Henry VI to be old enough to lead. It's a series of unfortunate events, for sure.
Rising Action
We'll Always Have Paris—Or Not
The English aren't doing so well in France, since Joan of Arc turned up to lead the French troops. She may be a witch, she may be a saint, but no matter what, she's pretty kick-butt. And she's definitely a complication. What are the English to do?
Climax
It's Always a Crisis
It's a little hard to say what exactly the turning point of this play is. There are a lot of crisis moments, and not so much decisive action, at least by Henry. Maybe the climax is Henry getting crowned king in Paris, but he doesn't do very much. Or maybe it's Talbot's brave but failed attempt to fight off the French army and York's later capture of Joan of Arc. When Talbot dies, after all, there's no longer an English hero capable of really holding off the French, nor can the French army can't do the job without Joan. This is definitely a point of no return.
Falling Action
Don't Wanna Fight No More
Well anyway, the English and the French negotiate for peace (they kind of have to at this point), and Henry agrees to marry a rich French noblewoman if it will help seal the deal. He's never seen her and isn't sure he's old enough to be married, but if it's good for his kingdom, why not?
Resolution
End in Tears
In the resolution, everything's supposed to get tidied up so we have a nice clear ending. Apparently Shakespeare and Co. didn't get the memo. At the end of this play, Henry breaks off his engagement and decides to marry a poor woman one of his nobles thinks is hot. The play ends with that noble, Suffolk, planning to manipulate the king by sleeping with the queen. Resolved? We think not. At least there are two more plays to explain what happened.