We are flying into Brussels, but will be leaving the same day to go to Amsterdam.
We want to take a train. What train should we take and how do we make reservations?

YOu can look up schedules via Belgian Railway website. there is no need to buy/book your tickets in advance.

http://www.b-rail.be/main/index.html

BTW, you need to change train once. From Brussels National Airport to Brussels Central, then change trains there for Amsterdam Central. Takes about 3 hrs 15 minutes.

Use the Belgian railways website to search for the right train and to make reservations:
http://www.b-rail.be/main/E/
The website is multilingual, including English.
I presume you would be leaving from the airport, which is Brussels Zaventem - you would select 'Zaventem airport' as your starting station.

P.S. If you want to spend a few hours to visit Brussels, you can take the train from Brussels National Airport into Brussels Central - drop off your luggage there - then walk down to GrandPlace. The train station has left luggage facilites (both manned booth and lockers). You can buy tickets for both train trips at the Brussels Airport rail station when you arrive.

You don't need to make reservations unless you want to pay more and take the Thalys on which reservations are compulsory. The International Express picks up at all three stations in Brussels and will get you to Amsterdam within minutes of the Thalys. The Thalys only stops at Midi on its way from Paris to Amsterdam. If you want to see a bit of Brussels before boarding you want to be at the Central station. It has luggage lockers and a manned check room.

Wow

This is all great information. Thanks. We are planning to spend time in Brussels after Amsterdam. My wife and I are really looking forward to this trip.

Thanks for all your help