Most efficient travel from Frankfurt to Trier

Train. obvious. Look up times and prices on the DB website: https://www.bahn.com/en/view/index.shtml
You want Frankfurt (Main) Flughafen to Trier.

There's guidance in the tour information that you get on this.

There are train stations at the Frankfurt airport from which you can easily get to Trier, with a couple changes.

We did a similar transfer a few years ago. We learned that the regional trains are about the same for journey time as the IC trains, but have much nicer scenery on the trip as they follow the river. You catch them at the regional train station at the airport (just follow the signs). It is very easy, with two simple transfers.

There are 2-3 different routes you can take... The most scenic route, the one to Trier via Mainz and Koblenz, follows both the Rhine and the Mosel rivers (for the most part) on the way to Trier. Eurailpass providers promote their products using photos of this route, the most scenic in all of Germany IMO.
http://static.panoramio.com/photos/large/12303966.jpg

You can also get to Trier most quickly by taking this route. I suggest you take it.

Route description:

Frankfurt airport - Mainz: pretty dull
Mainz - Koblenz: Good once you're outside Mainz; excellent between Bingen and Koblenz, where it follows the river the whole way. See train line map.
Koblenz - Trier: Very good, follows the Mosel almost all the way to Bullay; nice enough from Bullay to Trier as well. See map.

"you can easily get to Trier, with a couple changes."
It's easy enough to find trains with only one change of train (in Koblenz) if you want.

"We learned that the regional trains are about the same for journey time as the IC trains, but have much nicer scenery on the trip as they follow the river."

Carol might have heard this from someone but it's incorrect. First, there are no FRA-Trier train journeys that use only IC (or other high-speed) trains. IC trains from FRA to Koblenz are possible, but once in Trier you must board a regional train to reach Trier. And second, if you take an IC train to Koblenz it will definitely pass through the exact same scenic section as the regional trains to Trier.

It's probably best to take the regional trains. Any journeys that include high-speed trains will be expensive if bought at the airport (about €50 each.) Although high-speed train journeys can be pre-purchased as "saver fares", these fares are train-specific, and if you miss your pre-scheduled train at FRA because of a flight delay or whatever, you lose the ticket. The regional train tickets can be bought at the airport whenever you arrive at the FRA train station - and once there, you can normally take advantage of the regional day pass offers... with these a couple should be able to do the 3-hour train trip for around €40-€50 total.

Do you know what date and hour your flight will arrive at FRA? If so we can help you find a regional train schedule and provide more specific ticketing advice. (Not all the pricing options are shown at the DB web page that follows.) You can check train schedules yourself at the itinerary search link below.
http://reiseauskunft.bahn.de/bin/query.exe/en

FRA airport station: Frankfurt(M) Flughafen Regionalbf
Destination station: Trier Hbf

BE sure to click on "only local transport" so that the regional train itineraries show up properly. Once they do, click on the arrow at the left to get trip details (transfer station, time, and platform number.)

I'd figure in maybe an hour's time or longer within FRA after your scheduled arrival time. Remember that ANY of the regional train tickets available for purchase online are also available at the train station itself on your day of travel for the same price from ticket machines like these with an English language option. Pre-purchase = no price advantage on the regional train tickets. Again, feel free to re-post with your arrival date/time for further ticketing advice.

"We", assume you mean 2 of you. If you just buy regional train tickets to Trier, it will be 86 EUR for two. But you can also buy something called a "Quer durchs Land" ticket which will be 52 EUR for two. You can ride any regional trains in Germany to anywhere after 9 am weekdays. If you arrive on a weekend, you can also get a Schoenes Wochenende ticket and it is only 44 EUR for two and no time restriction. You have to buy these out of the ticket machine, or if from a ticket window, a whole 2 EUR more. So with these you can ride any regional trains from Frankfurt airport to Trier. You can even stop over along the way if you want.

Now, for advanced penny pinchers, there is a way to do this for even less. Buy 2 local RMV train tickets to Mainz, which cost 4.80 EUR each. At the same time, buy a Rheinland-Pfalz ticket for 2 costing 29 EUR. Take any regional train or S-bahn to Mainz Hbf, which the RMV ticket is good for. Then the rest of the way to Trier on regional trains via Koblenz, which the R-P ticket will be valid for. So total cost will be 38.60 EUR for two.

Week days, you are required to travel after 9 am, which should not be a problem as most flights arrive after 7 am, and after you get luggage and walk to the airport Regionalbahnhof, it will be after 8 am. The strategy using the combination RMV ticket and R-P ticket works better as the RMV ticket is not time restricted. The R-P ticket has to be used after 9 am weekdays, but it should be after 9 am by the time you get to Mainz (25 minute train ride), or very close to 9, so if you get there earlier, just wait until after 9 am before continuing on the Koblenz.

Note there are two train stations at the airport fairly close to one another, the Regionalbahnhof (the one you want) and the Fernbahnhof (long-distance train station). Trains from the Fernbahnhof are more expensive because they are IC and ICE express trains and you cannot ride these with the regional tickets. And they really don't get you to Trier any faster with these because you would be riding them for short stretches.

I don’t have any suggestions for transportation ( I flew in to Paris before my GAS tour) but I do hope you are coming in a night or two ahead of your tour start. This gives you time to accommodate any delays in your flights as well as time to recover from jet lag and travel fatigue. Plus I found Trier really interesting with more to see than what you have time for on the tour.

This is such a fun and interesting tour! I know you’ll have a great time.

Take any regional train or S-bahn to Mainz Hbf, which the RMV ticket is good for.
Then the rest of the way to Trier on regional trains.

You don't have to change trains in Mainz, just tickets. There are direct regional trains to Koblenz or Bingen that go through Mainz. As long as you leave Mainz after 9 AM on a weekday or anytime on a weekend day, you can stay on the train at Mainz. The RMV ticket is valid for travel to Mainz, where you can start using the RL-P-Ticket at 9 AM.

There is a direct RE (RE 4254) from Frankfurt Flughafen Regionalbf to Koblenz at 9:24. That train is scheduled to arrive at Koblenz on track (Gleis) 4 at 10:54. The RE to Trier leaves from track 9 (a one platform change) at 11:06.

Thanks Diane for posting this query, as I have had the exact same question and will be doing this tour in August. The responses have been incredibly informative and detailed (Russ, Lee, Sam)! My flight arrives at 10:55 into Frankfurt, and based on the extremely helpful information provided, it seems that it won't be possible to make the 16:00 tour orientation at the hotel, as the train leaves at 13:23 and gets into Trier at 16:30, plus the time needed to hoof it from the station to the hotel. So we will arrive a day earlier, and maybe even consider one of the suggested diversions on the way to Trier (but likely will be too pooped from the 9 hour flight and arriving at a biological time of 3 AM) and spend the extra night there.