Hangover Quests generally start off in a bar where the main character drinks heavily and eventually pass out. They wake up the next day missing some of their items and all memory of what happened the night before. After talking to each person they piece together more and more of what happened and sometimes have to pay for damages caused.
Dovahkiin gets challenged to a drinking contest by Sam Guevenne. They eventually wake up in a temple in Markath and have to help clean up the mess they made. Dovahkiin then has to reimburse Ennis for stealing his goat (or get the goat back from a giant named Grok). After heading to Whiterun, Ysolda tells Dovahkiin they owe her money for a wedding ring. They then travel to Witchmist Cove to find their new 'fiancée' who turns out to be a hagraven called Moira. After getting the ring from Moira by force, Dovakhiin travels to Morvunskar where Sam Guevenne reveals he is infact Sanguine, a Daedric Prince.
Geralt of Rivia spent the night drinking with three members The Blue Stripes after an arm wrestling match. He woke up the next morning without any weapons or clothing with a tattoo on his neck. He asks the Madam Margot about the night before, discovering he and the Blue Stripes attempted to sail the river on the backs of her ladies. He then gets his items back from Ves who had collected them and placed them in a chest in the Blue Stripes Headquarters. Geralt can talk to Triss Merigold in order to get a list of ingredients needed to remove the tattoo if wanted.