Brussels to Amsterdam

There is a regular route between Brussels and Amstedam, which you can catch at the Midi or Central stations in Brussels. If you know the specific date/time you want to travel, you can purchase advance tickets...but it's not that expensive to buy day-of. No reservations are required. http://ns.nl/en/travellers/home

You have multiple train choices from Brussels to Amsterdam. There are the NS high-speed services already mentioned, and the Thalys high-speed trains. The high speed trains can be cheap if you book in advance, but these tickets are for one train only and there are no refunds if your flight is delayed. Alternatively, you can get slower Inter-City trains which are cheaper if you want to buy tickets once you get to Brussels. You will also have to get a train from the Airport to central Brussels. There are three stations in central Brussels: Nord, Centrale and Midi (in that order as you come in from the airport). The higher speed trains only leave from Midi so make sure you get off at the right station.

Just to note, there are 2-3 trains per hour from the airport to all three stations in the city (the order of arrival is Nord, Centraal, Zuid). No need to buy in advanced, just buy the ticket after you pick up your luggage. The station is easy to find once you enter the arrival hall.

To avoid confusion, be aware that Midi and Zuid are two names for the same station.

We took the IC (Intercity) from Brussels to Amsterdam Centraal. 2 hours 50 minutes. The Thayls is 1 hour 50 minutes, so you save an hour. But we were connecting from Eurostar and the IC train was the soonest one leaving. We traveled 2nd Class and it was jam packed on a Friday. We had a big suitcase which was too heavy to place in the overhead compartment, so we had to leave it between us on the floor at our seats. With hindsight, we would have bought 1st Class tickets for a little more room and less people.