At the beginning of the story, essentially nothing happens. The narrator's interested in telling us about Mathilde (even though we don't yet know her name). We learn about her back-story, her character, and her unhappiness with her mediocre life. This represents a classic initial situation.
The action proper begins when M. Loisel (Mathilde's husband) comes home with the invitation to the fabulous ball and Mathilde reacts by having a fit. Now we have a specific problem: Mathilde's now has the best opportunity she's ever had to have a taste of the high life, but she has nothing to wear. That problem sets the rest of the plot in motion.
Mathilde solves the first problem when her husband gives her money for a dress. But then she runs into a second problem: she's needs to have some jewels. Luckily, her friend Mme. Forestier is able to provide her with a fabulous diamond necklace. But now Mathilde's been entrusted with something expensive that belongs to someone else and we have the potential for disaster. It's true that the complication is often when things "get worse," and that doesn't really happen here (for that, we have to wait for the climax). In fact, after borrowing the necklace, Mathilde has the time of her life. But it's when she borrows the necklace that the possibility opens up for something really bad to happen…and it does.
Mathilde's discovery is the most exciting and dramatic moment in the story (until that crazy twist in the last line). It's also the turning point in the plot. Before, the story was a build-up to Mathilde's one glorious night with the rich and famous. Now it transitions into a desperate search. We have a feeling things are not going to end well.
After the loss of the necklace, we're kept in constant suspense. First, there's the search for the necklace: will it be found? When it becomes clear it isn't going to be, the question becomes: what will the Loisels do? Will they find a replacement? And when they do, the question is: how the are they going to pay for it? It turns out paying for it takes quite a toll on them – their lives are ruined for ten years.
When Mathilde meets Mme. Forestier on the Champs Elysées, it looks like we're just about to tie up the last loose end in the story. The main action is over – the Loisels have finally finished paying off their debts for the necklace. All that remains is for Mathilde to see whether her friend ever noticed the substitute necklace, and tell her the sad story of the whole affair. But then things don't quite wrap up the way we expect.
Sometimes critics say that the twist ending is the climax of the story. You could think that the twist is the most exciting moment of the story, and represents a turning point since it reverses everything that came before. But we're sticking to our guns, and saying that the twist ending isn't the climax, but the conclusion. A climax is technically the point of the plot that everything builds up to, and that's not true of the twist. What makes the twist so effective is that by the time it happens the plot has already "risen and fallen," and seems to be wrapping up naturally. Then, right in the denouement, everything changes. Unlike your run-of-the-mill conclusion, this conclusion is exciting, and it upsets everything.