The explosive we're told would be used in this "scary plot" is TATP (triacetone triperoxide).
The Register tells us just how to make the stuff. Don't worry, the details aren't there to actually do it. But the details are there to tell you this "plot" was the "plot" that was not. Either that, or we have been misinformed about the nature of the explosive.
Below, here's what you'd have to do:
First, you've got to get adequately concentrated hydrogen peroxide. This is hard to come by, so a large quantity of the three per cent solution sold in pharmacies might have to be concentrated by boiling off the water. Only this is risky, and can lead to mission failure by means of burning down your makeshift lab before a single infidel has been harmed.
But let's assume that you can obtain it in the required concentration, or cook it from a dilute solution without ruining your operation. Fine. The remaining ingredients, acetone and sulfuric acid, are far easier to obtain, and we can assume that you've got them on hand.
Now for the fun part. Take your hydrogen peroxide, acetone, and sulfuric acid, measure them very carefully, and put them into drinks bottles for convenient smuggling onto a plane. It's all right to mix the peroxide and acetone in one container, so long as it remains cool. Don't forget to bring several frozen gel-packs (preferably in a Styrofoam chiller deceptively marked "perishable foods"), a thermometer, a large beaker, a stirring rod, and a medicine dropper. You're going to need them.
It's best to fly first class and order Champagne. The bucket full of ice water, which the airline ought to supply, might possibly be adequate - especially if you have those cold gel-packs handy to supplement the ice, and the Styrofoam chiller handy for insulation - to get you through the cookery without starting a fire in the lavvie.
Easy does it
Once the plane is over the ocean, very discreetly bring all of your gear into the toilet. You might need to make several trips to avoid drawing attention. Once your kit is in place, put a beaker containing the peroxide / acetone mixture into the ice water bath (Champagne bucket), and start adding the acid, drop by drop, while stirring constantly. Watch the reaction temperature carefully. The mixture will heat, and if it gets too hot, you'll end up with a weak explosive. In fact, if it gets really hot, you'll get a premature explosion possibly sufficient to kill you, but probably no one else.
After a few hours - assuming, by some miracle, that the fumes haven't overcome you or alerted passengers or the flight crew to your activities - you'll have a quantity of TATP with which to carry out your mission. Now all you need to do is dry it for an hour or two.
There is much more to the article. It references peer-review information on the explosive, why it needed mixing in-flight, ect. Read the whole thing here (same link as above).
For me, the net effect of the article is that, there is no way we are getting the whole (or even the right) story. *UPDATE* In the comments, Free Radical, rightfully, questions the "assumption" that the explosive in question was TAFT. The answer is: An article in Time [http://www.time.com/time/nation/article/0,8599,1225453,00.html] says the following:
Senior U.S officials have confirmed to TIME details of the plot that led the secretary to ratchet up the color-coded security alert for British-U.S. flights to an unprecedented red for "Severe." A total of 24 individuals were arrested in Britain overnight and, says one senior U.S. official who was briefed on the plot, five still remain at large. Their plan was to smuggle the peroxide-based liquid explosive TATP and detonators onto nine different planes from four carriers -- British Airways, Continental, United and American -- that fly direct routes between the U.K and the U.S. and blow them up mid-air. Intelligence officials estimate that about 2,700 people would have perished, according to the official.