To be honest, the best way to work out what happens in the story is to read it for yourself, but as you seem to be rather pressed for time, let me summarise it briefly for you. In this excellent tale by Nathaniel Hawthorne, the elderly physician Dr. Heidegger invites four old friends to his office to experiment with a potion of eternal youth that he has acquired. The guests, as befitting the allegorical nature of the tale, all represent various vices of humankind. For example, Colonel Killigrew represents lust and hedonism, having wasted his life in "sinful pursuits". Mr. Gascoigne is a ruined politician who represents hypocrisy. Mr. Medbourne is a merchant who lost everything after some foolish specultation, represents greed. Lastly, Widow Wycherly represents vanity. The other three guests had been in love with her in her youth.
Dr. Heidegger restores a dead rose with the potion then each guest drinks of it, becoming younger and fitter and healthier. The men compete vigorously for the attentions of the Widow who has become beautiful again. However, the effects of the potion soon wear off and the guests are devastated by their ageing. Dr. Heidegger explains the point of the experiment - given their youth again, the guests fall in to the same mistakes they made first time round, so he has learned the benefits of age and appreciating what you have learnt by watching their foolishness. However, the guests have not learnt this lesson - they determine to hunt the Fountain of Youth in its source to be able to be young always.