Train from Amsterdam (AMS) to Ghent - step by step

If you've never taken a European train this site is a very useful primer: https://www.seat61.com

You won't want to buy your tickets in advance, since there's the risk of delay, causing you to miss your booked train. Buy them at the airport train station.

We just last month traveled Schiphol to Ghent coming from our flight inbound flight.
You can buy tickets in advance for the convenience of not having to buy tickets in line quickly while trying to make a train, if you do not take the Thalys. Tickets for the regular trains can be used on any regular train that day. The costlier (unless booked well in advance) Thalys, while direct, is train seat specific.

Your first train taking regular intercity trains is Schiphol to Rotterdam. There are numerous trains, some more direct than others. Takes from about 35 minutes to near an hour if it is not direct. Your change is Rotterdam is to simply move over a couple platforms. The direct Intercity to Antwerp appears to be hourly, at 10 after then hour, and takes just over an hour. the train from Antwerp to Ghent is hourly at 37 minutes after, giving you 22 minutes to change tracks and also take a little time to view the Antwerp Centraal Station, which is one of the most beautiful train stations in the world. The train from there to Ghent will first arrive at Daamport, and depending on where you are staying, may be only 1/2 the distance or less to your hotel, rather than going to Sint-Pieters, which is a longer distance into the center of the city. Your ticket will be good for either of these.

We bought our tickets on a combination of the Dutch website and the Belgian website, this led to the least fees. Note that unless something has recently changed, you do not have to pay the supplement for traveling to Antwerp by way of the Rotterdam train as long as you have that ticket also.You can book a costlier Thalys for direct to Brussels from where you would then have to switch trains to Ghent, that train arrives first at Sint-Pieters.

When we went, our connection to Amsterdam was delayed in departure due to fog in Amsterdam, so it was a good thing we were booked on the locals, we would have missed our connection. The rail station in Schiphol is easily accessed.

The advantage of the Intercity train over the Thalys is, as said above, the ticket is valid for all trains that day. In case your flight is delayed, you can easily take the next train.
The Thalys service comes with a mandatory seat reservation. A full-price ticket allows for a change of trains, but will still involve making a new reservation at a service desk. An advance-bought discounted ticket is train-specific, and in such a case worthless.
In Ghent both the Dampoort and Sint-Pieters stations have a taxi to the city centre. From Sint-Pieters the fare is EUR 10 or less.

I take it you could not fly to Brussels. I believe that the Thalys option would require the expensive "Any Belgian Station" add on, or buying a retail day ticket at the Brussels Zuid/Midi station upon arrival and taking one of the very frequent local trains (without luggage racks) to Ghent. (Don't misunderstand that: NO Thalys-branded train carriage goes to Ghent, although some go to Antwerp.) If you post again, give the month of travel and the day of the week you are flying in.

Most destinations in Ghent require a local bus ride, but the ticket machines are right outside the station. If your bags have good wheels, look at Google Maps and see if you'd want to walk. Rick has general Euro train advice top left blue menu.

This is not a particularly hard trip, but it would help to know if you have ever been to Europe or traveled by train there. I will say that sometimes the announcements on domestic Netherlands trains are not in English, but negotiating stations is very easy, no harder than negotiating an airport. All the track numbers are arabic numerals, after all. Have you seen the wall-mounted composite paper schedules before? I mean yellow and .... the other color - Arriving and Departing?

the wall-mounted composite paper schedules
Better use the train planner of the Dutch railways. It gives all information on possible connections, including the track they're leaving from. Not all trains going to Rotterdam have it as final destination, making the electronic departure board somewhat confusing.
By the way, Dutch railway stations only have departure schedules (in the standard yellow), while most European countries also have arrival schedules (in the standard white). Don't ask me why.

tom, I was talking about orienting oneself in the station, especially if you didn't understand the announcement about the platform number. Those sheets have the (normal) platform number, as well as general guide to the next few trains, in case you missed the one you were counting on. I was just trying to offer the OP a calming thought process, out in the field!

I understand, but - with the exception of the direct connections with Rotterdam as final destination - only the train planner makes clear what possible trains to take.

Thank you all for your help. It seems simple enough. We have traveled by train in Europe, but it has been a few years. The flights from our US home city to Brussels were all two connections at least, took about 3 hours more, and cost about $1,000 more than just a round trip to Amsterdam (where the RS tour ends). So we thought we would rather take a nice train ride from Amsterdam to Ghent, save the money and enjoy ourselves more. Love riding trains and looking at the countryside. Since we are getting in a day early and the train seems so easy, we are going to search for a nice town to stop in on the way to spend the night before heading into Ghent. Even a town out of the way would be fine - as long as we can walk to the train station to a hotel and back. Again, thank you all for your help. If anyone has suggestions on a town to visit along the trip, that would be much appreciated.

I absolutely loved Delft - small town south of Amsterdam, not very busy during the day but very quiet at night. Should be either close to or on the train line heading south to Belgium. There are direct trains from Schiphol to Delft most of the time.

Because Rick goes to Delft and not to Antwerp, Antwerp would be my choice. Delft is "too far" for fearless departure (I'm speaking conceptually, not about mileage) the same day as a cruise or tour. Antwerp is not a small town, but a very rich visit destination and less urban than Brussels. Leuven is a much smaller city, with good train connections, but enough to do for one day. Lier requires a train change, but has a smaller medieval center.

Note that all these medieval centers are surrounded by modern cities, if not quite "high-rise." I happen to like medieval centers, but someone else might not need to see four or more on one trip! Because you are talking about less than 24 hours in your destination, and including a night in bed, I don't think the exact choice is critical. It is exceptionally easy and fast to get from Brussels or Antwerp to Delft. If Leuven has the pleasant illusion of being a smaller place, it's not hard to get to Ghent but I think you have to change in Antwerp or Brussels. All these trains go multiple times per hour on business days.

Day of the week? Don't forget museum closures especially Monday.

I would say that Antwerp and Amsterdam have some points of similarity, except for number of waterways. But that includes being great places to visit.

Oh - and sorry - I forgot to say, we will be arriving Sept. 11th this year, which is a Tuesday. We expect to land in Amsterdam around 1pm.

Note that your early September travel dates are very close to Open Monument Days (Open Monumentendagen) in the Netherlands, Brussels, and Flanders (which may have different dates.) This can require sifting through mostly Dutch pages, but it's easy to learn of seldom-open and abandoned places that can only be visited on those days - if you are interested and have the time to do the research.