This is the formal confession prayer that is repeated ten times throughout Yom Kippur, and once on Erev Yom Kippur at Mincha. Vidui includes:

Ashamnu: – We recite a litany of confessions in alphabetical order, striking the chest lightly at each mention. While it does not enumerate specific sins, it is good practice to mention one’s sins at the appropriate letter. For instance, if one ate a prohibited food, he might say “achaltee davar assur” – I ate something prohibited, after reciting the word “Ashamnu”, since those words also begin with the letter Aleph. Each sin should be placed in its appropriate place.

Al Chait – This is a much more detailed confession that begs forgiveness for specific sins. When reading this confession, one should think about past wrongs committed, and repent from sins that pertain to each confession.

Note that the tenth and final Vidui that is recited during Chazaras Hashatz of Neilah includes only Ashamnu and not Al Chait. The other nine, as well as the Vidui recited on Erev Yom Kippur, include both.