The Canterville Ghost, otherwise known as Sir Simon, planned to take his revenge on the Otis family is the standard ghostly fashion. He plans to scare them out of his house. Many, many years ago, Sir Simon killed his wife. He gives a ridiculous reason for the murder too.
"My wife was very plain, never had my ruffs properly starched, and knew nothing about cookery."
In response, Sir Simon's brothers-in-law starved him to death. He has been haunting the mansion and its owners ever since.
Sir Simon starts out simple with the Otis family. He causes a blood stain to keep reappearing despite the Otis's best efforts to get rid of the stain. Then he appears one night rattling his chains and making ghost howls on another night. In each case, the Otis family calmly suggests a way for Sir Simon to stop being so noisy.
"My dear sir," said Mr. Otis, "I really must insist on your oiling those chains, and have brought you for that purpose a small bottle of the Tammany Rising Sun Lubricator. It is said to be completely efficacious upon one application, and there are several testimonials to that effect on the wrapper from some of our most eminent native divines. I shall leave it here for you by the bedroom candles, and will be happy to supply you with more, should you require it."
Eventually the Otis family starts having fun with the ghost of Sir Simon, and the twins actually begin terrorizing the ghost. It's a hilarious turn of events. Sir Simon keeps trying to up his terror factor and tries to get more and more elaborate with his costumes and scares. He eventually brainstorms about being something truly terrifying.
This last insult so enraged him, that he resolved to make one final effort to assert his dignity and social position, and determined to visit the insolent young Etonians the next night in his celebrated character of "Reckless Rupert, or the Headless Earl."
It's all to no avail. The Otis family simply will not be scared by him. Sir Simon eventually makes peace with them and his lot in "life," and he accepts eternal rest with the help of Virginia Otis.