If a doctor tells a person that he is certain to die shortly (e.g., within one hour), what should that person do during his remaining minutes?
Various siddurim and halacha books have recommended "last rites", so to speak. This is done between the individual and G-d; if a rabbi is present, that would only be to help the person read the material. It usually include an affirmation of faith (in various wordings, often paralleling Maimonides' Thirteen Principles), an expression of confession (to G-d, not to the rabbi) and request that others forgive him, and the Shema.
Good question! Obviously saying Vidui would be on the short list of things to do.
The truth is that this question is relevant to all of us, every day, as illustrated in this story:
The Kelmer Maggid, in one of his stirring and fiery shmoozen, painted the following mental picture for his audience: imagine that Mashiach would come to the Beis Hachayim - the cemetery - and announce to all those buried there that they had been granted one hour of life...imagine the stampede that would follow, as all the "newly living" dash to the nearest Beis Hamedrash to learn, daven, and perform as many mitzvos as possible. No seductive material temptation or enticing conversation would be attractive enough to distract even one of those individuals for a slight moment. They were given one hour, and they were totally immersed in their opportunity to earn priceless zechusim - merits - for eternity. They would do this by investing every breath and every thought in spirituality and the fulfilment of mitzvos.
After describing the scene in vivid detail, the Kelmer Maggid turned to his audience with a roar and said, "und vos is az men hot mer vi ein sho - and so what if we have more than one hour? Un ver vaist zu men hot takke mer vi ein sho - and who knows that he certainly has more than one hour to live?!"