Getting a train from Frankfurt Airport

Bought tickets yet? You can get a Rail & Fly ticket that will include any rail connection after your flight to anywhere in Germany, but I believe you have to buy it when you buy your airline ticket.
https://www.bahn.de/p/view/mdb/bahnintern/services/mobilitaet_service/rail_fly_airrail/mdb_274276_20180628_railandfly_airlines.pdf

If that is not an option, you will clear Schengen immigration in Iceland, so it will just be a domestic flight. Get off, go to luggage carousel and collect your bags and proceed to the Fernbahnhof (long distance train station). I'd say 1 hour is safe, but whether or not your plane will arrive on time is the most important variable. You could be delayed arriving in Iceland and miss the connection, or the connecting flight could be delayed.

Full fare tickets are 114.50 EUR per person. Direct ICE trains take 3 1/2 to 4 hours. If you want to travel cheap, you could use regional trains taking 5 1/2 to 6 1/2 hours for less than the cost of a single full fare ticket for up to 5 people. Depends on how many people are in your family, their ages, and if you arrive on a weekend or a week day. Totally flexible, just buy at the airport train station.

You can get a Rail & Fly ticket that will include any rail connection after your flight to anywhere in Germany, but I believe you have to buy it when you buy your airline ticket.

Depends on the airline. It is certainly worth a try even if the ticket has already been bought.

If they are flying with IcelandAir, this airline uses terminal 2, so they will need to go to terminal 1, where the long distance trains are. Taking the bus may be the most efficient way for them to get there as it stops right outside of the rail station.

I would plan 45-60 minutes after landing before reaching the right train station (see details below):
luggage: 20-30 minutes
change terminal 15 minutes
go to train station 10 minutes

If you chose a flexible fare ticket you can take any train on chosen route (recommended because you do not know if and how much a flight may be late).
Overview of fares: https://www.bahn.com/en/view/offers/index.shtml?dbkanal_007=L04_S02_D002_KIN0059_TOP-NAVI-ANGEBOTE_LZ01

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Details:

Map of FRA airport: https://www.frankfurt-airport.com/content/dam/airport/Dokumente/Lagepl%C3%A4ne/Terminal-%C3%9Cbersicht.pdf/_jcr_content/renditions/original.media_file.download_attachment.file/Terminal-%C3%9Cbersicht.pdf

There are two train stations. They need to chose the "Frankfurt am Main Flughafen Fernbahnhof", not the regional station.

Map of the Fernbahnhof station:
https://www.bahnhof.de/resource/blob/1038862/aab455ca2045985d190c5040567c728c/Frankfurt-am-Main-Flughafen-Fernbahnhof_locationPdf-data.pdf

As already mentioned the station is in front of terminal 1, part B. So they need to get to there first. Advices here ( would prefer the short Skyline train, free of charge):
https://www.frankfurt-airport.com/en/travel/transfer.html#transfer

From 1B they need to take the bridge walk along the Sheraton hotel https://goo.gl/maps/nbh15BPfHqy

This video shows how to get from T2 to train station by bus (not my priority but possible):
https://www.youtube.com/watch?v=bhFwSEknZkc

Between terminals I've walked and bused, haven't done the sky train. I found walking disorienting particularly after transatlantic flights. I suspect getting to and from sky train would be a similar experience. Bus is easy, go to the appropriate location outside, get off go in and down (to the regional station)

Between terminals I've walked and bused, haven't done the sky train. I found walking disorienting particularly after transatlantic flights. I suspect getting to and from sky train would be a similar experience. Bus is easy, go to the appropriate location outside, get off go in and down (to the regional station)

"I suspect getting to and from sky train would be a similar experience."

Very easy, just follow sighs "Terminal 1 / ZABC".

I have never heard of anyone walking between these 2 terminals!

If you don't have luggage, the SkyTrain is fast and easy, but there are multiple escalators going up (2x) and down (2x) and up (1x) and down (1x) if you choose this way of getting to the long distance station from terminal 2. The bus is ever so much easier with your bags. It comes every 15 min. Stops directly in front of terminal 2 and stops directly in front of the long distance train station.

There are not only esclators, also lifts, so very comfortable - easier than getting all that into a bus and holding that and yourself in my experience.

Thank you for your responses!

All of your information has been helpful in forming a plan to get to the train station and having a good understanding of the time frame.

Thank you again!