Frankfurt to Holland via train
 

I am flying into Frankfurt from the US arriving on a Monday 20-Jun morning around 08:00. I need to then train travel to The Hague.

1). Will it be straightforward to find the long-distance train station and procure a ticket to The Hague? Do I buy at a ticket counter or via a machine?
2). I looked into buying my train ticket in advance but learned that if I miss my train due to my being delayed (or spending too long in airport customs), that I forfeit my ticket. How long after landing should I anticipate to get to train station (carry on bag only)?
3). The train journey appears to be 5 - 6 hours with 3 - 4 train changes; is this tricky or easy to navigate?

Much thanks in advance for your suggestions and help.

I'd fly FRA to AMS and then a 30 minute train ride to the Hague

Are you using bahn.de for train schedule? Looks like it's possible to go from Frankfurt airport (Flughafen) to the Hague (Den Haag) in four and a half hours with one change, but there are three hours or so between those trains.

All you need to know about train travel in Europe is here: https://www.seat61.com/european-train-travel.htm

Quite apart from the environmental problems with that given the mess at Schiphol nowadays I would not fly to Ams. They are also cancelling many intra Europe flights, often at short notice.
One does wonder why OP chose Frankfurt, rather than Schiphol, or even Brussels.

There are fully flexible tickets available for trains, at a cost, and if that ticket is for ICE trains then you can use it on other trains as well without changing the booking. No doubt Bahn.de will tell you all about it if you try a test reservation. There is an ICE/IC route so only one change but whether that is a convenient time only you can say.

Also whilst technically you are visiting Holland, since Den Haag is in the province of South Holland, the country is the Netherlands.
Note the Hague in Dutch is either Den Haag or 's-Gravenhage on signs.

I don't know how long the queues are at FRA nowadays, but if it were me, I would wait in line to speak to an agent who could select the best train option. The best option is really the non-stop to Utrecht, then connecting directly to Den Haag, but one leaves at 830am and the next one doesn't leave till 11:42. The problem with others is not only the multiple connections, but you might wind up on regional trains that tend to be PACKED nowadays because of the 9-Euro ticket. Speaking to an agent can help you avoid long stretches in virtual sardine cans, and minimizing changes (consider too a longer lunch break along the way, if it makes for more comfortable segments).

On your way from the arrival zone of the airport to the railway station (Fernbahnhof) you will see 2 Ticket corners (DB Reisezentren) where you can get your ticket from human beings.
Don't worry about crowded regional trains due to the 9 Euro ticket. Nobody will sell you a regional train ticket for the Frankfurt airport - Dusseldorf leg.
From there to the Dutch border you may have to use regional trains indeed, but these latter are run by Eurobahn or VIAS Rail which don't accept the 9 Euro ticket anyway.

I think I used various schedules, but certainly do not recall an option with only one time change. Or if so, maybe that was too early. I will land FRA around 8:30 or 09:00.

You should use the schedules at bahn.de, since that is the German railway company. In normal times you could make the 11:42 train, these days, who knows how long immigration will take?

Thanks to everyone for the helpful advice

Agree your best option for train travel from FRA to Den Haag is the ICE 156 departure at 1142 am to Utrecht where you have a five minute transfer to IC 175 for the short 38 minute train to Den Haag. Given your schedule this seems like a reasonable time to allow you to arrive, clear immigration, collect your bags and get to the airport train station, picking up your ticket on the way. You'll probably even have time for a coffee.