While there are various customs concerning the order of the Viduy prayers, or different additions, the underlying theme remains the same. We have presented a common format below. One may also add prayers or Psalms as one wishes.
Try to recite the entire Viduy. If it is not possible, say at least from Adon Olam onwards. If one is even further pressed, one should recite the verses from Shema Yisroel onward. The least one should do is say "Let my death be an atonement for my sins," and recite the verse of Shema. (these prayers are to be found in Prayers for the Final Moments)
Hebrew and Transliteration:
Translation:
I acknowledge before You, Lord my G-d and the G-d of my fathers, that my recovery and my death are in Your hands. May it be Your will that You heal me with total recovery, but, if I die, may my death be an atonement for all the errors, iniquities, and willful sins that I have erred, sinned and transgressed before You, and may You grant my share in the Garden of Eden, and grant me the merit to abide in the World to Come which is vouchsafed for the righteous.
Our G-d and G-d of our fathers, may our prayers come before You, and do not turn away from our supplication, for we are not so impudent and obdurate as to declare before You, Lord our G-d and G-d of our fathers, that we are righteous and have not sinned. Indeed, we and our fathers have sinned.
We have transgressed, we have acted perfidiously, we have robbed, we have slandered. We have acted perversely and wickedly, we have willfully sinned, we have done violence, we have imputed falsely. We have given evil counsel, we have lied, we have scoffed, we have rebelled, we have provoked, we have been disobedient, we have committed iniquity, we have wantonly transgressed, we have oppressed, we have been obstinate. We have committed evil, we have acted perniciously, we have acted abominably, we have gone astray, we have led others astray. We have strayed from Your good precepts and ordinances, and it has not profited us. Indeed, You are just in all that has come upon us, for You have acted truthfully, and it is we who have acted wickedly.
One may add the "Long Confession" found in the Yom Kippur prayer book.
Following the Confession, recite the following:

Master of the universe, may it be Your will that my passing be in peace.
Concentrate strongly on G-d and His unity,and on the event of the giving of the Torah on Mount Sinai.