Dear Young Tourer,
sadly enough, wild camping is a rather grey area in German law. If you put up your tent someplace you like and nobody shows up to shoo you away, perfect. However, my German fellow citizens like to be very duteous and might either report you or directly call the police when they see you camping while they walk their dog or something. As I said, it is a grey area and you never know what people will do if they catch you
Things are different in Sweden, for example, where there is the so called "allemansrätt" which basically means that you can camp on any ground that does not belong to anyone for 1 or 2 nights, making sure you pack everything you brought and that you don't litter the place or make a big bonfire. Not sure about small fires, you might want to look that up, not sure about any other northern European countries.
However, having made this really negative, camp sites in Germany are open to cyclists and the most I ever paid for putting up my tent, the bike and using the washrooms were 15€, which sounds a lot, but I could take the longest shower ever ;-) They are usually also equipped with washing mashines, tumble dryers etc. Depends on the campsite and their prices, of course. When wanting to tour Germany on one of our official trails get the respective copy of the respective trail guide from Bikeline or the Kompass Radführer(it does not let me post the links), we have those guides for most German bike trails. They give you everything from camp sites over hotels, b&bs and other information about mileage and altitude etc.
If you need anything else, feel free to email me as I live in Germany... I also have an overview map which features all of the official German long distance bike rides, I can easily make a couple of pictures of that map and send it to you. Just tell me if that would be of any use to you!
Germany is a beautiful country I, myself, have just started to discover and riding your bike in Germany is a great thing to do!
Best wishes,
Anne