You really need to get a map of the area. Google maps are good, because they come with a satellite view. You can see the castles, the bus stop, and the train station. If you go to www.Bayern-Takt.de and select "Englische Version", you can get station plans including Google maps and satellite views.
Both castles, Hohenschwangau and Neuschwanstein are in the village of Hohenschwangau, about 10 minutes from the train station. You get to Hohenschwangau from the Füssen Bahnhof by taking the bus, so you will need to buy the ticket BEFORE seeing any castles. The bus lets you off in Hohenschwangau just down the street from the kiosk where they sell the tickets to the castles. I'm sure other people from the bus will be going there too. As I remember, there is a counter just for English, or at least non-German, speaking visitors. After seeing the castles, go back to the bus stop and take the bus to the Bahnhof.
I seem to remember that in 1988 my German Rail pass covered the bus to Hohenschwangau, but that was then and it was not a Eurail pass, but try it. Show your Eurail pass to the driver and see if he takes it. And let us know. He might let you ride even if the bus isn't covered just to be nice, particularly if he doesn't speak English and can't explain why the bus isn't covered.
There are trains leaving the Munich Hbf at 7:51, 8:52, and 9:51, from the Starnberger Flügelbahnhof, Gleis (=tracks) 27-36. The Starnberger Flügelbahnhof (wing station) is just outside the main shed area of the station on the north side. If you arrive on the S-Bahn, there is a direct set of stairs (or escalator) from the S-Bahn station, or you can get to it from the middle of the platform of track 26. It's really not this complicated; I'm just trying to give you every detail.