To get a short and comprehensive summary of Emma is a bit of a trick, especially if all characters are of importance. Peripheral characters will of necessity be omitted, yet you can fill them in in your own summary, which this summary will only be a guiding reference for.
Almost twenty-one years old, Emma loses her friend and governess, Miss Taylor, when she marries and becomes Mrs. Weston. Emma, having "rather too much her own way" and thinking a "little too well of herself," finds a replacement for Miss Taylor's lost companionship in the newly befriended Harriet Smith whom Emma decides to groom for a higher social class. Though Harriet is romantically attached to farmer Robert Martin, Emma decides she should instead be attached to the vicar Mr. Elton. Mr Knightley, Emma's neighbor, friend and the patriarchal overseer of Highbury as owner of Donwell Abbey (and benefactor and friend of Robert Martin) warns Emma that she is inappropriately relating to Harriet while ignoring other relationships that are worthy of her notice.
Just as Mr. Knightley predicted, Emma's efforts with Harriet backfire when Mr. Elton, who has long been in love with Emma--humoring Harriet only to please Emma--proposes to Emma in her carriage on their way homeward through the snow after a party at the Weston's home. Emma rejects him. Emma is shocked.
"You have made yourself too clear. Mr. Elton, my astonishment is much beyond any thing I can express."
Elton is outraged. Harriet is heartbroken. Elton goes off to Bath and later brings back to Highbury a bride. While Harriet is beginning her protracted period of weeping, Jane Fairfax and Frank Churchill (Mr Weston's natural son raised by the deceased wife and mother's family) both make their appearance in Highbury. Even though Jane receives a mysteriously delivered pianoforte while Frank is inexplicably in London, no one has reason to connect the two.
The entrance of Mrs. Elton and her bustling friendship with Jane leads to a strawberry party, an outing to Box Hill and a ball, which all result in the revelation of secrets between Jane and Frank, Harriet and Mr. Knightley, and Frank and Emma, while Mr. Knightley has secret plans for farmer Martin. At the strawberry party, Mrs. Elton pressures Jane to accept a governess position (putting Jane in a compromising position) and Jane and Frank quarrel. The quarrel is slyly continued at the Box Hill outing while Emma thinks Frank is showing a romantic interest in her. Emma insults Miss Bates thus earning a scolding from Mr. Knightley, who shows his manliness by dancing with Harriet at the ball after she is scorned by Elton.
The story soon after resolves with the truth about Frank and Jane's secret engagement coming to light following Mrs. Churchill's death. Emma realizes Mr. Knightley was again correct in warning her that Frank was insincere in his attentions. Mr. Knightley facilitates the engagement of Harriet to Robert Martin, and Emma realizes she loves Mr. Knightley and that he mustn't marry anyone but her, which is convenient because he knows he mustn't marry anyone but Emma.