Conflict enters the scene when Mrs. Elvsted visits to the Tesmans on a trip to the city from her country home. She’s there looking out for a guy named Eilert Løvborg, a recovering alcoholic who tutors her children. Hedda, the master of manipulation, soon gets Mrs. Elvsted alone and coerces her into admitting the truth: she and Eilert are somehow involved, and she wants to leave her husband for him. Eilert has just published a book – he’s in the same field of history as Mr. Tesman – and Mrs. Elvsted has followed him to the city to make sure he doesn’t fall back on his old drinking ways. She begs the Tesmans to look out for him, since George is his colleague and friend.
Shortly after, Judge Brack, the big man around town, comes by and flirts with Hedda. It’s clear he’s interested in her. Everyone keeps asking Hedda the same question: why has she, the best catch in town, married a bore like George? Hedda admits that 1) she had to marry someone and 2) she thought George, through his scholarly pursuits, would be famous some day.
Eilert eventually stops by the Tesmans and we discover that Hedda has a history with him; they used to be intellectual buddies the way that Eilert now is with Mrs. Elvsted. When Hedda broke off their friendship/budding romance, she did so to avoid the scandal of hanging out with a questionable, renegade alcoholic like Eilert. She also threatened to shoot him with one of her father’s pistols. Now that he’s with Mrs. Elvsted, Hedda decides to entertain herself by causing some trouble. She tells Eilert that Mrs. Elvsted was afraid he would drink again – in other words, she doesn’t trust him. This angers Eilert, who promptly starts drinking again. He goes out to a party with the Judge and Hedda’s husband George, but not before revealing a tantalizing and plot-thickening tidbit: he’s written another book, this one using information from the past to predict the future. He’s written it with the help of his new muse, Mrs. Elvsted. He has the only copy, a hand-written manuscript, with him now and will read some aloud tonight.
Mrs. Elvsted stays with Hedda, worried sick that Eilert will drink himself silly at the party. Of course, Eilert drinks himself silly at the party. He never returns that night. While Mrs. Elvsted is sleeping, George comes back early the next morning, tells Hedda about the drunken debauchery, and shows her something: Eilert’s manuscript. It seems that Eilert dropped it while drunk and George recovered it, eager to keep it safe so he could return it to his friend once sober. When a letter comes regarding Aunt Rina’s fading health, George rushes out, leaving behind the manuscript.
Later that morning, Eilert comes running in. Mrs. Elvsted wakes up in time for him to break up with her, telling her that he tore up the manuscript and doesn’t want to see her any more. Mrs. Elvsted declares that he has destroyed their child (meaning the book) and leaves. Only then does Eilert admit, to Hedda, that he lost the manuscript. Hedda, being Hedda, says nothing about the recovered manuscript and instead gives him a pistol with which to shoot himself. She’s eager for Eilert to have a beautiful, poetic death – she wants him to shoot himself in the temple.
Finally alone again, Hedda burns the manuscript to ashes. When she confesses this to George later, he is overjoyed that his wife loves him enough to destroy the work of his professional rival. Mrs. Elvsted visits again the next morning to find out what’s going on with Eilert, and Judge Brack comes by to tell everyone that Eilert is dead by suicide. Mrs. Elvsted and George, feeling quite horrible, decide to re-write the manuscript using Mrs. Elvsted’s notes. While they start work, the Judge takes Hedda aside and tells her that Eilert didn’t commit suicide – rather he accidentally shot himself in the gut. Hedda is devastated that the great poetic death she imagined never came to pass. Brack also reveals that the pistol firing the fatal shot was Hedda’s –he recognizes it. He can keep this info quiet, but only if she does what he wants.
No one tells Hedda what to do. She shoots herself in the temple.
(Totally quoted from http://www.shmoop.com/)