There are many ways to explore Germany, depending on your itinerary, personal taste, and budget. Germans are the people that invented the term Wanderlust and travel in Germany is proof that it's not always about the destination, sometimes it is the journey.
Note that German trains and most busses don’t automatically reserve a seat! If you want to get a good seat, don’t arrive at the bus or train station late.
Train. Trains in Germany are operated by Deutsche Bahn (you can buy tickets on their website). Despite its bad reputation among Germans, it’s a comfortable way of getting around the country.
Pros: comfortable, relatively fast, two classes of transportation to choose from.
Cons: not very reliable as trains often get delayed, not cheap (although there are discounts).
Bus. There are several European bus companies that run their services all over Germany with the most popular one being Flixbus (many buses + cheap prices).
Pros: cheap, many routes to choose from, efficient, pretty scenery outside the window.
Cons: rather slow, not very comfortable for long rides.
Pros: some low-cost flights, direct flights to long distance destinations will save you time.
Cons: most flights are expensive, indirect flights will cost you time, getting to/from the airport only adds trouble.
Pros: flexibility, nice way of getting around when travelling with a group of people.
Cons: gas and parking fares are expensive, parking rules are strict.
Renting a car with driver
Pros: flexibility, you don’t have to worry about parking rules and such.
Cons: very expensive, not a common service so it might be hard to find.