Coffee beans are first softened in hot water or steam. Then caffeine is dissolved from the beans by using a solvent such as methylene chloride, ethyl acetate, or a gentler solvent such as water itself.
Liquid carbon dioxide is a much more expensive alternative, but has the added advantage that it does not remove the flavour molecules.

Removing caffeine from coffee

Health

The solvents used to obtain decaf coffee also remove some of the flavour molecules. These are then added back. 
One way is to perform a first extraction with water, then shake up the water with a small volume of methylene chloride, or pass it through a charcoal filter. Both processes selectively remove the caffeine from the water but leave most of the flavour molecules.

decaf

Removing caffeine from coffee

How is caffeine removed from decaf coffee? - BBC Science Focus Magazine