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
Merton Densher and Kate Croy are in love. Yay! But Kate's rich aunt Maud has forbidden them to marry. Boo! This is because Merton is a poor commoner, and Maud will cut off Kate's financial pipeline if she keeps locking lips with Mert. And Kate seriously needs the cash: her dad is a penniless mess and it's the turn of the century, so she can't exactly go out and get a job.
So Kate and Merton decide to get secretly engaged and wait to tie the knot until they can think of a plan to win over Aunt Maud. Just when they seem to be getting their act together, though, Merton gets called away to the United States on business.
Act II
The book suddenly jumps from following Kate Croy and Merton Densher to following Milly Theale—a young, beautiful, and rich American girl—and her friend Susan. The two are traveling through Europe for some fresh air because Milly has discovered that she's ill. Like dying ill. It turns out that Milly met Merton in New York and has fallen in love with him.
Milly drags Susan to London, where Susan gets in touch with an old school friend: Kate's Aunt Maud. Small world, right? Anyhoo, Merton eventually comes back and sees Milly in London. His fiancée Kate realizes that Milly is: 1) in love with Merton, and 2) very ill. For this reason, she encourages Merton to seduce Milly and eventually marry her so that he can inherit her fortune when she dies from her illness. Merton doesn't like the idea, but he goes along with it in a hesitant way.
Act III
Milly gets word that Merton and Kate are secretly engaged, and the news breaks her heart so much that her illness gets worse. Merton has a chance to deny his engagement and love for Kate (in part because it might postpone Milly's death), but he can't do it. He leaves Milly and later hears that she has died. On Christmas Eve, he gets a letter in Milly's handwriting and gives it to Kate, asking her to open it for him.
It turns out that, even though Milly knew Merton was deceiving her, she loved him so much that she left him her money anyway. Merton, though, isn't satisfied to take the money and marry Kate. Instead, he tells Kate that she can either take him as he is (read: poor) or she can't have him at all. He vows never to touch the money if she marries him. The book ends on an unclear note and doesn't tell us one way or the other what Kate's final decision is.