Once you arrive in Germany, if you are American, you will notice that the German public transportation system is much more efficient and cost effective than that of America. There are many more options and for the most part, you can get anywhere any time. Keep in mind that you can purchase a train ticket from your current location to your destination and this ticket is valid for the train, bus and street car. ie. Take a train from Darmstadt to Hanau then use the same ticket for a bus from Hanau to Frankfurt.
Taxi Cab: Taxi cabs can be found around any airport or public location. If you walk up to a taxi parking area and there is a row of taxi cabs go to the front vehicle first. The price varies but can be expensive at times. The weekend taxi fees are generally more expensive than the fees on a weekday. If you can avoid using a taxi cab I would recommend it. If you are relatively pleased with the service provided by the cab driver a one or two EUR tip would be sufficient.
Street Cars (Trolley): Street cars were the first mode of public transportation in Germany. Street cars make frequent stops and have a map layout of each stop. Check the route and be sure the stop you want is close enough to your destination, if not you may want to take the U/S Bahn, a bus or a taxi. Street cars are relatively fast, about the same speed as a normal car in the city.
Train: The European rail system is set up to be a very cost effective and efficient means for international European travel. With a vast number of inner-city trains running constantly during the day, the German train system is just as effective. When entering a train station (Bahnhof) you will need to purchase a ticket from the machine. You can only buy a train ticket with EUR but you can use any denomination below 20 including coins or bills. Simply select your destination from the list shown, enter the destination number and push the 'Einzelfahrt' button. Your change will fall along with your ticket to the tray. If you are planning to travel by train from Frankfurt to Paris, for example, you may choose to use the ICE train. This train is designed to get you from point A to point B much faster than a normal train. ICE trains are a little more expensive but may be the smart way to travel if you are planning inter-country travel in Europe.
U/S-Bahn: The U or S Bahn would be the equivalent to the subway in the States. The U-Bahn covers city areas where as the S-Bahn covers city areas and up to 60 kilometers outside the city. Normally you will only find U/S Bahns in bigger cities. The U/S Bahn normally makes more stops than trolleys making them the smarter choice for inner city travel.