When we arrived from the US to Frankfurt, it was easy to take the train from the airport to Bacharach, Go to Terminal 1 underground, track 2 of the regional train. Reader boards show next train arrival. Buy ticket from ticket machine. Machine shows English. Look up Bacharach. Purchase with card. We took the R 2 to Koblenz. Get off at Bacharach, before Kiblenz. From Bacharach can go to St. Goar on Koln Dusseldorfer cruise line. Leaves daily at noon in high season. Buy tickets from ticket office on warf. If water levels are low, go to St. Goarshausen and take ferry back across Rhine to St. Goar.
The Deutsche Bahn app is also easy and wonderful to use. One can review options ahead of time and purchase tickets. Hopefully you were able to secure the 9€ ticket which is accepted on the regional trains, buses, trams, s-bahn, etc and good Deutsche Bahn for travel in Germany for an entire calendar month (ending in August).