Help with Transportation: Munich to Fussen to Regensburg to Prague

Train schedules and advance ticket discounts for longer trips are all on the German web site. How to Look Up Train Schedules and Routes Online gives you the DB train schedule link and tips for using it. But there's no requirement to book trains ahead or until you are ready to commit to dates and times. Perhaps the last trip is the one you'd book ahead.
A group of 4 traveling on slower regional trains just within Bavaria can also buy a cheap Bayern Ticket in the train station, about 52 euros for all day.

Keeping the car as far as Regensburg is an economical option for 4 travelers. Three days often costs the same as 1 or 2 when booking ahead. Auto Europe is a good starting place to check rates from several European vendors.

Thank you, Laura! Just the guidance we needed.

"My question is: What are the train options?"

Getting to Fuessen by train is easy and cheap. There are 4 of you. Are any of you kids? The Bayern Ticket for 2 adults and 2 kids under 15 is E28/day. The Bayern Ticket for 3 adults and 1 kid is E33. The Bayern Ticket for 4 adults is E38. (I do not know where the price of E52 in the first response above came from.) The BT is valid all day (weekdays, all day after 9 am.) You can verify the prices and details here at the DB page:

https://www.bahn.com/i/view/USA/en/prices/germany-regional/bavaria-ticket.shtml

Once you are in Fuessen, you can use the same Bayern Ticket that same day to catch a bus to the Neuschwanstein/Hohenschwangau stop (8 minutes) - or anywhere else you have a mind to visit - no extra charge.

You can use another Bayern Ticket for the train ride to Regensburg as well.

The Bayern ticket is valid also for inner-city transport, so if you need a bus or a tram you are covered.

Trains don't go to every mountain town. Do you have other outings from Fuessen you plan to make?? If so, there's probably a doable bus schedule, but you should share your plans here. We can probably tell you whether a car is needed. (There's a lot of nice scenic walking you can do around Fuessen too, btw.)

A lot of us North Americans choose a car for a trip to Fuessen and elsewhere for "recreational" driving or because (like you) they/we are underinformed or confused about train options. We don't vacation by train at home at all, and we all understand just how cars work, so the choice of a car is usually not so much a "preference" as it is a reflex action for most of us.

You might need a car - but there's no way to know without more details about your outings from Fuessen (if any.) For Munich-Fuessen-Regensburg, the train, at E56 - E76 total , is a sure bet. Gas alone for those legs will be E40 or so, plus parking, plus rental fees and insurance, plus your pick-up, drop-off time/hassle, the rental contract...

Here is a map of the area immediately around Fuessen with marked train and bus lines:
http://bilder.fuessen.de/uploads/pics/streckennetzplan-750px_02.jpg

There might be some low cost options from Regensburg to Prague. What day of the week do you have planned? If on a weekend, a Bayern-Boehmen Ticket could work. On week days, 9 am is too late a start to get you to Prague in a timely manner.

The direct ALX train from Munich (9:01) to Prague (14:41 or 2:41 PM)) stops in Regensburg from 10:20 to 10:31. A Bayern-Böhmen-Ticket would be valid any day on that train as far as Pilsen.