It would vary quite a bit. During the nineteenth century, it was possible for individual travelers to purchase mummies and ship them back to Europe without any interference from customs authorities. So, the most common sort of mummy unwrapping party would be a standard Victorian dinner party held by a friend of yours who has recently return from his travels abroad. Instead of showing photos, he would regale you with tales of his journey. As the featured event of the evening, he would bring out the mummy he had purchased, place it on a central table (could even be the billiard table in his games room) and remove the bandages any way he could. During the process, he would attempt to spook you with stories of ancient curses or impress you with his knowledge. At the end, the mummified dead body would be on display. The overall effect could be either one of a learned lecture or of telling spooky stories around a campfire.

The second type was a form of public spectacle. You would be invited to an exhibition featuring artifacts returned from Egypt (i.e. looted) and, after having traveled through the exhibit and dined, a sarcophagus would be brought out and opened with great ceremony. The mummy would be slowly unwrapped by someone with considerable expertise. The jewelry and protective amulets found within the wrappings would be shown to all and passed around. Some exhibitors even had a rotating stand which they could place the mummy on, so they could unwrap the mummy with great flourishes and show all sides as the body was slowly unveiled. After the body was unwrapped, you would be invited to come closer and gaze into the face of an ancient prince/priest/whatever. Giovanni Belzoni, a former circus strongman who was a prolific looter/Egyptologist, is perhaps the most famous of the showman-type unwrapping party throwers. (See "Popular Exhibitions, Science and Showmanship, 1840-1910" by Jill A. Sullivan, pp. 206ff)

The third type was the most exclusive and was part of a meeting of a learned society such as the Royal Asiatic Society or the Mechanics Institution and involve the "great and the good" of society (aristocrats, bishops, doctors, et c.). Such an unwrapping would be considered essentially an act of scientific study by scholars and accompanied by a lecture. You would be gathered around the mummy, which could be in its original sarcophagus or only in its bandages. The speed of the unwrapping could vary quite a bit, depending on whether those gathered were interested in the nature of the wrapping itself or in the body and the mummification processes involved. Those with the talent would be called upon to sketch the unwrapping as it proceeded with the idea of presenting the sketches as a record of the procedure or as the plates that would form part of a scholarly publication. The person doing the unwrapping would be a doctor or surgeon. Once the body was unwrapped, it would be examined minutely by the participants to determine what could be learned anatomically and about the mummification process (although some participants would likely be more voyeuristic than scientific). The body and its wrappings was usually donated to a museum after the party. Thomas Pettigrew became quite famous during Victorian times for this type of mummy unwrapping party, and wrote about such parties in the introduction to his book "A History of Egyptian Mummies, and an Account of the Worship and Embalming of the Sacred Animals by the Egyptians; With Remarks on the Funeral Ceremonies of Different Nations, and Observations on the Mummies of the Canary Islands, of the Ancient Peruvians, Burman Priests &c" published in 1834.

Qualifying question: was the Victorian era really the "height" of Egyptomania? I thought it was in the 1920s.

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