The primary airport in the Netherlands is Schiphol. There are other lesser known airports but unless you have a private jet or you spend the same amount as business class for flights less than 1 hour long then I would forget about any other destination. Schiphol is an international airport and almost all airlines go through it, located southeast of the Amsterdam Central. There are various forms of transport to get you out of the main complex:
Train
Taxi
Bus ooh and obviously Planes.
The place is open 24 hours and hosts a small village for shopping, drinking, eating and relaxing. There are many terminals and the complex is very large. The most common UK - Amsterdam airlines will go through terminal 1.
::UPDATE::
As of 1st August 2003 KLM NO longer offer free travel with NS Rail.
There's sculptures all over the place here!