I think they dissolve it out in liquid carbon dioxide under very high pressure.
The process takes a few of the flavour compounds too, but is surprisingly effective.
Can't see the point myself...
Caffeiene is taken out from the unroasted coffee beans by a water or solvent process. In both cases caffeine is brought to the surface of the beans by treating the green beans with warm water and steam. In this method the unroasted bean is soaked in a water solution which removes caffeine along with other water soluble componants. In a seperate step this mixture is filtered through activated charcoal (the swiss water process) or through a solvent like New Forester says either way this is how it is done, the swiss water process leaves you with a much better flavour and some people say they can not tell the difference!
Kind of get where your coming from NF with regard to the point, but I have high blood pressure and have been told to cut down on caffeine, but love coffee, so it's ideal for people like me. Until recently instant coffee was chemically decaffeinated, and filter could be either chemically or water decaffeinated, but now Nescafe decaff in red jar is done with water and tastes really good (for an instant coffee). Read that the chemically decaffed is really bad for you (for your liver I believe).