Dutch trains are great. They are clean and fast and not that expensive. And very busy at peak periods. But given the endless traffic jams and impossiblity of finding a parking space, they are the best way to visit another city. If you are going to the centre of The Hague from Amsterdam, you will need to change at Leiden otherwise you will end up at the out of town station Den Haag HS.
Keep an eye on your luggage if you are going to Schiphol by train. Schiphol - Amsterdam Lelylaan is a popular bit of track for bag snatchers. If youths in baseball caps are hanging around the first class carriage, ask yourself why.
The revamped NS website has a route planner etc in English, plus an online demo of how to use a touch screen ticket machine.
For high speed trains to the continent - don't be fooled. There are no high speed trains in Holland yet. The website for the stupidly-named hispeed company which is supposed to operate them says it is offering a brand new concept. Laughable.