First of all hitchhiking is very popular in Germany. If you want to get this way across the country (for example from Hamburg in the north to Munich in the south) expect to make the journey within two days, although, with a little bit of luck, it is also possible to make it in one day.
Germany has very good freeway system connecting all major cities. Like in most countries the drivers are forbidden to pick up hitchhikers AT the freeway (Autobahn). Therefore you need to catch a car at the entrance to the freeway. All you need to do is to hold a sign with the symbol of the city you are going to (HH = Hamburg, H = Hanover, M = Munich, B = Berlin, K = Köln, etc). Usually you will get picked up pretty soon. However, if you are trying to catch something at the main thoroughfare, it is often worth to be “choosy” and not get into the first car that wants to pick you up, if the driver does not go far enough to justify it. Try to catch a car that will cover at least one third of your total journey. Otherwise you may end up an hour later standing at the road again, maybe in a worse place, with many competing hitchhikers, particularly if you go to a popular destination. However, I have to admit that the hitchhiker community in Germany is rather fair and the ones that arrive at the spot first usually will get picked up first, unless the driver has “special” wishes…
Time-wise hitchhiking is a gamble. Therefore if you want to better predict your travel time, it is good to call “Mitfahrzentrale”. It is a service, available in most bigger towns and cities, linking drivers and passengers to share the cost of travel. Unlike hitchhiking, this type of travel is not totally free but it is still very cheap, as all you pay is the cost of petrol plus a small service fee. “Mitfahr” (which means "drive with") makes particularly sense when traveling grater distances.
German railway service (Die Bundesbahn) is very fast, dependable and can be relatively inexpensive. Include Saturday or Sunday as one day of travel and save by getting “Supersparkarte” (Super-Saving-Ticket) which gives you return ticket for a very low price. If you cannot travel on Saturday or Sunday, then it is often cheaper to buy two return tickets each one containing Saturday or Sunday as traveling one of the directions.
If you also travel to other European countries, the best idea is to buy Eurotrain ticket, which will give you 15 days of travel across most of the countries anytime within a two-month period! All that at a very low price!
Accommodation in Germany