I also want to mention that while I was around for all but 5 days of the 1960s, I don't actually remember this particular craze. Perhaps I was just too young in 1966 when the paper dress was invented by the Scott Paper Company as a marketing stunt. Nobody there expected too much to come from it, but this became a fashion craze and for around $8 you, too, could own one of these disposable creations. And you can have an original one still, but it will cost a bit more today.
According to my primary source, wikipedia, you could even get a paper bikini! Not sure how you might swim in one. Of course, this was not actual paper, like newspaper, or copy paper, but a kind of disposable cellulose fabric.
Now if you were a creative type, and wanted to make your own, Simplicity was there to help you out with Simplicity 7376! Released in 1967, the Jiffy "easy cut-easy sew" caftan was suitable for paper and felt, in addition to, well, regular fabric. On the instruction page, there are a couple of hints on just how you should treat the sewing of paper. For one, to hem the dress, you simply mark the hem and cut it off at the desired length. What could be easier?!!
The short, sleeveless dress (view 3) has a bit of a hospital gown feel to me, and the general unattractiveness and lack of durability were a couple of factors leading to the quick demise of this fashion fad.
Did you ever have or wear a paper dress back in the day? Would you wear one today?