train from amsterdam to munich

Buying at the train station is THE most expensive way to buy a ticket, just like at airports. Tickets go on sale 3 months before your intended travel date at www.bahn.com. Cheapest will be tickets for a specific train, and you can print the tickets at home, or even load them on your smart phone. ICE is InterCityExpress, top line German train.

It will be cheaper to buy the ticket in advance. But, of course, once you buy a ticket you can't change your mind and travel on a different train. Not without loosing money.
Buy your ticket from the company operating the train, DB (German Railways): https://www.bahn.de/p_en/view/index.shtml
Resellers may charge more and/or offer a limited choice. If you buy online you can get a "print-at-home" ticket. Then you just get on the train, and show the ticket you printed plus the credit card for ID.

ICE is the German Railways brand for High Speed Trains. ICE international are the ICE trains that travel outside Germany. Sleek shiny trains that look like this: https://www.raileurope.com/cms-images/468/593/ice-overview-3.jpg

As a for instance, the fastest route would be 7 1/2 hours and require 1 train change in Duisburg or Duesseldorf. Two tickets tomorrow at the station will set you back 342.40 EUR. If you bought them 3 months in advance, it would be 139.60 EUR. The train for this route follows the median of the A-3 between from just outside of Bonn to just outside Frankfurt and will hit over 200 mph. You'll pass those Mercedes on the A-3 that are doing 120 like they were standing still.

But in your shopping, you might notice that there is a train route that requires 2 train changes and takes 8 1/2 hours, but costs only 78 EUR for two people. This one follows the Rhine River past the Lorelei and all those castles. Much better scenery at half the price.

Or you can fly to Munich in an hour. Starting early next year, KLM's budget affiliate Transavia will be flying that route for 39 to 43 Euros--quick, easy, cheap.

Thanks for all the tips. Sam, do you know how I find the longer route along the Rhine?

When you look at the schedule at www.bahn.com, you will enter the start and stop points, date, and time (say 08:00) and the number of travelers, then click on "search" and you will get the first 3 possible trains starting about 8 am, to see later trains, just click on "later".
The list will show the departure and arrival times, total travel time, number of changes, types of trains, price if you buy specific itinerary now "savings fare", and the full price fare. Below you'll see "Show details". click on that it will show where each leg stops and starts and how much time to change trains. Then click on "intermediate stops" and you will see all the stops along the way.
So the 8:05 train leaving Amsterdam Centraal, you will see it stops at Mannheim and you change there for a train to Munich. When you look at all the stops, you will see it stops at Siegburg/Bonn and you know it travels the east side of the Rhine away from the river and (with some inside knowledge I guess) on the median of the A-3 on special high speed tracks.
Now look at the next train, it also starts with the 8:05 from Amsterdam Centraal, but this time you change trains at Duesseldorf going to Mannheim and checking the intermediate stops you see it stops in Koblenz. Koblenz is on the west side of the Rhine and you know (sorry, from experience) that it goes right along the west bank of the Rhine River. You'll see it arrives in Mannheim an hour later than the other train.
You can also click on the "map view" and you will see a map of the route. Click on "station information" and it will show diagrams of the stations where you change trains and end, and also in some cases, local transit networks.

Short story, use the route details to see where the individual legs of each itinerary goes.

There is a »Map view« button at the bottom of the details window showing the exact route.

I agree that if you want to take the train, the route along the Rhine is worth the extra hour.

If you haven't checked out this website, it is THE BEST in train travel information. Hope it helps: http://www.seat61.com/

Back in April I took that same route on the CNL night train which was awesome. Left Amsterdam at about 10 PM (dont remember the exact time) and arrived in Munich around 7 or 8 AM. This provided us a lodging and transportation while allowing us for a full day in Amsterdam and waking up for a full first day in Munich. I highly recommend it. You can spend as much or as little as you want, meaning you can spend the night in a standard train seat, you can buy bed in a 5 bed couchette (shared room with other travelers) or you can get a private compartment with 2 beds and a sink. Just go to the Bahn website and it's very simple to book.