Hey Lucy ... just for this time I won't ban you
... but, it's just
this time.
From a purist point of view caffeine-free coffee is not
real coffee. It's a warm beverage that tastes like coffee. It was coffee one day, but it is not coffee anymore... because someone took out the caffeine from it.
It is not a synthetic stuff that's sure!
How to remove caffeine from a coffee bean?. Well, take the bean (a non-roasted one), boil it for some time, rinse it with an organic solvent and that's it. You have a caffeine-less bean... weell yes, it has also lost many other compounds that can also be solved in water. That's why purist say, it's not real coffee, and that's probably why I, as Markus, prefer the hard and pure stuff.
You can find a quick description of the different descaf processes following Markus' link.
Other thing, caffeine can easily be extracted from tea leaves by sublimation: Take some black tea leaves, crush them, put them into a spoon and heat them with a flame... gently and slowly! After some time the leaves will begin to smoke. Put a glass over the smoke and you will see cafeine crystals forming in the surface of the glass. The tea will be useless (burned) after that, but hey, it caffeine-free!
(That was a experiment we did in the University when I took a phytochemistry course. However, a a more complicated process is needed if you want the pure stuff).