Frankfurt airport catching the train

The airport train stations are within walking distance from the airport (the regional train station is beneath Terminal 1, the long-distance train station is a few minutes further away), the main station is not. Just use bahn.com to look for a connection, using "FRA" as departure station. This will give you connections from both airport train stations.

If you fly in to Terminal 2, there's a shuttle bus to take you to Terminal 1, where the airport train station (Frankfurt Flughafen) is located. Get off the bus, cross over the street and go in the door and up the escalator. Turn right at the top and the corridor will take you right to it...and you will run into the Deutsch Bahn ticket office right by the train departures board. You can grab a local to the main city train station (Frankfurt Hbf). If you are going to Munich, you can grab the ICE train right from the airport. Check the DB website for schedules. Tons of trains, both Regional and ICE stop at the airport.

Jack's description is for getting to the long-distance train station (Fernbahnhof). The regional station is even closer to the mentioned bus stop. Or just follow the signs - no need for the bus if you arrive in Terminal 1.

Everything is connected; you can walk.
But fair warning: Frankfurt is a HUGE airport, and with your luggage, it could take you 15 minutes to walk to the ticket windows and another 15 minutes to walk to the train platforms. Then it’s a matter of finding the correct platform and the right train. It will also take you a few minutes to puzzle out the details and buy your tickets. DO NOT buy tickets for a train that leaves 10 minutes later. Give yourselves at least 30 minutes, or you’ll be completely frazzled and might get on the wrong train. Take this advice from someone who’s done exactly that (cough!).

Tip #1 - Google your flight to see which terminal you will be landing in. This will help you know how to get to which ever train station you need.

Tip #2 - Think about if you really want to sit on a train for a few more hours after a trans-Atlantic flight? I know I wouldn't.
Tip #3 - If you stay overnight in Frankfurt, you can buy those cheap ICE tickets (buy 3 months ahead) to cities like Munich for the next day without stressing about whether or not your flight will be delayed making your miss your train. Leave early the next morning and you will be in Munich by 10:00 after a good nights sleep. You will have been able to walk around Frankfurt and sightsee a bit, helping you get over your jet lag.

Stacy, that is probably a question of personal experience and risk aversion :-) Admittedly, I know the airport and the railway stations reasonably well, and I fully agree that it is huge. But I have managed a) walking from one of the most remote gates in Terminal 1 to the regional train station, with hand luggage, in about 10 minutes, and b) on another occasion, to buy a train ticket from the counter at the long-distance station, for a train that departed three minutes later - it was on time, and I caught the train. Both required a rather brisk walk, though :-)
On the other hand, checked luggage can take very long in Terminal 1 (45 minutes after landing is not unusual, and it can even take longer than that). And it definitely takes time to familiarize yourself with the airport. So the advice given by you and Ms. Jo definitely makes sense - just wanted to give a different perspective as well.

I just tried inputting "FRA" into the from box on the Bahn Query webpage. The choices I got did NOT include the airport. Put in "Frankfurt" and it will show you multiple choices including "Frankfurt(M) Flughafen Fernbf". That, the Fernbahnhof, is the long distance train station where you would catch an ICE to Munich.

Are you doing this flight with FF miles, and Munich is not an option? If you want to go to Munich, you really should be flying to Munich.

Do you already have your tickets? If you are flying on one of many participating airlines, you can purchase a Rail&Fly ticket along with your plane ticket which will allow you to go to any other train station in Germany on the day of arrival or the next day, for 33€/P. That way you can take advantage of a low fare without risking losing your ticket if the plane is late. I don't know if you can add Rail&Fly to an already purchased ticket.

If you can get a Rail&Fly ticket, I would recommend going on the Munich right after arrival. It's about a 3½ hr trip. There are direct trains (no changes) at least every hour, and these trains terminate in Munich, so you don't have to worry about falling asleep and waking up in Budapest. Freiburg is closer (about 2 hrs), and there are also direct trains, but they don't terminate in Freiburg, so if you fell asleep and missed Freiburg, you'd end up in Switzerland. The connection to Rothenburg might be a little complicated for someone who's sleepy and not familiar with the rail system in Germany.

But if you can't get a Rail&Fly ticket, staying in or near Frankfurt is not a bad idea. Last year I flew into Frankfurt on my way to a small town in southern Bavaria, which was 4½ hrs from Frankfurt and 90€ p/P for a full fare ticket. So instead I went 1½ hours with a local fare to St. Goar, spent 2 nights there, then used a Saver Fare to get to my ultimate destination.

I don't know if you can add Rail&Fly to an already purchased ticket.

That depends on the rules of the individual airlines not on DB. E.g., Lufthansa allows booking of a R&F ticket any time, other airlines only when booking the flight ticket.

I just tried inputting "FRA" into the from box on the Bahn Query webpage. The choices I got did NOT include the airport. Put in "Frankfurt"

You do not need to select any of the auto-complete options. Just enter FRA, do not make any selection, and the connections offered will start from one of the airport train stations.

Jack's description is for getting to the long-distance train station (Fernbahnhof).

Correct However, the Regionalbhf is not under T1, it is under the building across the access road from T1. You do access it from T1, by going down stairs or escalators just inside T1 and through a passageway under the access road. Most connections to Munich will leave from the Fernbahnhof. You can leave from the Regionalbahnhof, but that would require a change of trains in the Hauptbahnhof in Frankfurt.

If you do come into T2 (non-Star-Alliance airlines), there are two ways to get to T1 and the train stations. You can take the aforementioned bus, which leaves from the sidewalk outside T2, or you can go up to the top floor of T2 and take the shuttle train (Skyline) to the top floor of T1, and go down the stairs in T1. Both ways are about the same time, on average, but the bus runs an irregular schedule (approx 6 per hour).