Tail:
* The dog wagged its tail excitedly as it saw its owner. (referring to the appendage at the back of an animal)
* The plane's tail was damaged during the rough landing. (referring to the rear end of an aircraft)
* She couldn't resist the urge to gossip and tell all the juicy details of the story, especially the juicy tail end. (referring to the final part of a story)
Tale:
* The old man told us a fascinating tale about his adventures at sea. (referring to a story, often a fictional one)
* The book weaves a tale of love, loss, and redemption. (referring to a story told in a book)
* They spun a tale of woe to try and get sympathy from the judge. (referring to a story, often a fictional one)
Important Note:
While "tail" and "tale" are homophones (they sound alike), they have very different meanings. Using one when you mean the other will completely change the meaning of your sentence.