Using the train: DBahn

Most of the time for the tickets you will be using to get around it will be easiest to buy the ticket at the machine or the BAHN website which will tell you times, tracks and connections.  Your origination station will always be: Landstuhl bahnhof any city that has more than 1 train station will have and HBF - this is the main, big train station.
A great website that gives loads of information Getting around Germany: Train

Using the Bahn machines – Found the screens in German, but if you push the English button they will be in English – only take CASH; they will often not read a US credit card.

Traveling on the weekend in the area, it is best to use the Regional ticket - Rheinland-Pfalz ticket

First, on all screens

Suchen means "search",
Abbrechen means "cancel" (lit. "break of"),
Hilfe is "Help", and
Zurück means "back".

Let's see what you get when you press "Gesamtes Angebot"

This is the opening screen you will see on one of the Bahn automats. Clockwise from upper left:  Start-Zeil is where you enter information to buy individual tickets. Gesamtes Angebot (all offers) Here is where you can purchase regional (Länder), freetime, savings, and business travel tickets. You can also retrieve tickets already purchased. You can buy group tickets and weekly and monthly passes. Verkehrsverbund Here is where you can buy tickets for the local transit district, here the Rhein-Main-Verkehrsverbund (Frankfurt metro) Fahrplanauskunft Here you can print out the detailed schedule for a connection. You can also purchase reservations without a ticket.

This is the screen for "all offers". Next, let’s get a Länder ticket. Go to the screen for Freizeit und Aktionen. The top one should provide you with the Landes ticket for the region you are in, in this case Rheinland-Pfalz. Enter how many people over 15 are traveling with you and then pay in cash

Freizeit und Aktionen Here is where you can purchase Rheinland-Pflaz- and other Länder Tickets, such as the Bayern-Ticket. You can also purchase other regional offers. Spezial- und Sparangebote Use this to find Sparpreise and Europa-Spezial tickets. Service und Zusatzkarten Pay the supplement for night train reservations. Gruppenkarten Here for the Schönes-Wochenende-Ticket. Here also discounted ticket for groups of six or more on regional trains.