A couple of fairly substantial chairs (or elegant trestles, or anything that can support the weight of the assistant) are placed upon the stage. A board is laid across their tops and some drapery is placed upon it. An assistant — usually female as they don't weigh so much! — lies upon the board. S/he is "hypnotized" (hence the name Trilby's Couch) and urged to fly. The performer removes the chairs, one at a time — to a small distance as he will have to replace them - the board with the assistant on it moves up and down, tilts this way and that, and if the illusion is well done can move forward and backwards as well. Eventually the board floats down to its original position on the chairs, the assistant is revivified, and everyone is appropriately awed.
Quite simple in concept but difficult to execute properly. The drapery on the board is necessary to provide a little leeway for concealing the insertion of the rod. The performer walks behind the board after the assistant reclines on it, ostensibly to make sure she is comfortable and secure, but in reality to distract attention from the movement of the rod; also to make sure it's securely attached to the board. The assistant behind the scenes does all the hard work!
Naturally any astute member of the audience is going to suspect something of the sort. So the performer walks around the board at the appropriate times and passes a hoop over its length at others. There are two ways to accomplish this: one is to have the rod have a large horizontal piece extending most of the way to one end of the board, in the shape of a very thin "U". In this case the performer has to do a bit of misdirection at the end of his pass of the hoops so as to conceal the fact that he doesn't quite go all the way, and extreme care must be taken to make sure no part of the extension ever shows. A simpler method is to have a rigged hoop that can be opened up just enough to get past the bar. The apparent path of the floating board must be sufficiently varied to conceal the fact that it's actually moving around the fixed point of the rod.
This trick has been around for a long time. It's better known as Thurston's levitation because he popularized it in the U.S. He also patented it and the plans can be purchased from the U.S. patent office.
It has also been improved upon quite a bit since it was first presented. Nowadays it can be performed out of doors, with stage crew etc. being unable to penetrate the secret; as well, some performers (such as Doug Hemming) don't use a board on chairs: they start off with the assistant simply standing there, "mesmerized", and gradually levitate him/her off the ground to the horizontal position and whirl him/her about. The performer still doesn't let anyone get too close and the assistant isn't moved that far from a particular spot.