A guy decides to nuke a pizza. When the microwave dings, the pizza has been replaced with a brass lamp. So the guy starts rubbing the lamp. (After all, if he doesn't, the movie never starts, and we all watch something else instead) Predictably, a genii (or jinn, if you prefer) pops out of the lamp. In fact, she really pops out of the lamp. I'll leave the rest to your imagination. (or your entertainment if you watch the movie)
The dude (I think his name was Justin) seems reluctant to take the entire situation seriously -- in fact, one of his first wishes is for the genii to make a pizza for him, since the pizza he tried to eat had disappeared, and he was still hungry. His next wish was for the genii to tell him nine stories. He then notes to the audience that with the 'wrap-around' story they were showing now, that makes ten stories for the buyers.
So, for the rest of the movie Justin (or whatever his name was) and the genii are sitting on a couch, chatting, drinking, and even flirting a bit, while the genii tells Justin various tales. Like most anthology movies, some stories are pretty good, one or two are clunkers, and the rest are tolerable. My favorite was probably the "hard-boiled detective" tale, where the detective was hired to remove a ghost. The whole segment was filmed in black-and-white, with enough snappy comments to make you want to burst out laughing. (Imagine an old Sam Spade or Philip Marlowe movie with Bill Murray as the lead)
Is it a great movie? No, not really. But it is kind of fun.
One last note: If you check the credits at the end, it looks like several of the various stories were filmed anywhere from a year to three or four years before this collection was assembled. I'm not sure if that means anything significant, but I thought it might be worth bringing it up.
