Train from Frankfurt to Trier

Depending on your connection you go either to the station for regional trains (Regionalbahnhof, inside terminal 1) or to the one for long distance trains (Fernbahnhof, approx. 200m outside terminal 1). Usually, for that connection, it's a waste of money to pay the premium for the ICE, so I'd take regional trains. You may be able to save a fews Euros by splitting your ticket into a S-Bahn ticket to Mainz (available at a RMV ticket machine or via the DB app) and a Rheinland-Pfalz day ticket for the Mainz-Trier leg (easiest to book via the DB app).

Here's a link to the train information from the Frankfurt airport site that should give you some additional details to what sla019 told you. https://www.frankfurt-airport.com/en/transport-and-parking/by-train/local-public-transportation.html

Because those two rail stations are right there at the airport (Frankfurt Flughafen), there is a manned ticket office with english-speaking agents who can help you figure that out if not clear.

If you go to You Tube and search for “Frankfurt Airport Train Station”. You will find several videos about how to find and use the train station after arrival. I found these helpful when I made this same transfer.

We took the Flix bus from Frankfurt to Trier. It was a lot cheaper and faster. They have a stop at the airport, past arrivals C. This is direct, no changing of buses like you have to do with the train.

I tried to look up the trip by Flixbus from Frankfurt airport to Trier, and it said, "No trips. Due to the current Covid-19 situation, our trains and buses are not operating on a regular schedule."

But they did offer me a trip from Frankfurt Hbf to Stuttgart (sigh).

But that is what I remember from checking before. Flixbus only offers a few trips per day; sometimes not every day. So it might take less time on the bus, but you might spend the saved time waiting for the bus.

But if the schedule works for you and saves money ..... .

If, as Russ suggests, you might want to stop in Bingen on the way, buy an RMV (Frankfurt transit district) ticket to Bingen. They are only 8,95€ for an adult. Then when you leave Bingen for Trier, buy a Rheinland-Pfalz-Ticket, an all day ticket valid for any regional trains in the state of Rheinland-Pfalz (Trier is in Rheinland-Pralz) for 25€. (If you were going directly to Trier in one day, you would still buy an RMV ticket to Mainz for 5,20€ plus an RL-P-Ticket anyway, so it wouldn't be much more expensive, ticket wise, to stop overnight in Bingen instead of going straight through.

For that matter, you could go to Bingen Stadt, take the boat down to St Goar, spend the night there, then continue on the next day with the RL-P-Ticket