When first came to Germany to study, there were a number of guides available that gave overviews of the paperwork that one might need, notes on facts about certain types of registrations that are required, and other rather broad strokes of being a student in Germany. While largely useful, there are a lot of finer details which often get lost in these guides. Check out the pages below, where I'll be taking a swing at filling in some of the gaps that I've noticed in my years living and studying in Germany!
In the U.S., once you start a degree or study program, your continued registration in the program, assuming you are earning passing grades and don't have any other extenuating circumstances, is essentially automatic. Obviously, you still have to pay your tuition and any other fees to continue, but your studentship is not otherwise in question. In Germany, you have to rematriculate every semester, and you're on your own to make sure it happens.
One of the reasons that many people give as to why studying abroad is difficult for them is the costs associated with doing so. I was lucky enough during my time studying abroad during my undergraduate studies to receive a scholarship from my college, which helped to defray the costs. The Deutscher Akademischer Austauschdienst (DAAD) is the German government's organization which exists to provide scholarships for foreigners to study within Germany, and for Germans to study internationally. If you are American but aren't a dual citizen of a European country (and therefore are ineligible for the ERASMUS program for European students studying in other European countries), then applying for one of the programs through the DAAD is the primary option.
When you're looking ahead to the exams that you are going to take while in Germany, it's worth looking into the number of points that a given module, lecture, or seminar is worth, as unlike many U.S. colleges and universities, there is not usually a set number of courses that you have to take in a semester to reach "full time" student status. Germany, as with the rest of Europe, operates on the European Transfer Credit System (ECTS), and assigns a point value to each lecture (exam), seminar (presentation or essay), and lab course (lab report).
When you start at a Germany University, there are a lot of notable differences, from a total lack of a "traditional" campus, to oddities in exam registration, to the total lack of orientation courses for new students. Even for international students, exchange students, and, yes, brand new German university students. What are you to do?
When you register for a college or university course in the U.S., do you expect to have to register for the exam separately from registering for the course you're taking? Of course not! The registration for the course and the exam are one and the same. Depending on what and where you are studying in Germany, this is likely not to be the case however.
When you fill out your application or matriculation paperwork at a German university, you will likely notice that the grade section seems to be set up for people with absolutely abysmal GPA's, with the highest grade listed being a flat 1.0. After getting over your initial confusion, you likely had to put your grades through a conversion chart, only to (hopefully!) find out that the number was closer to 1 than that 4.0 we strive for in the U.S. system. What gives?
If you sign up for a language course, seminar, or full module at a German university you'd better be prepared for some public speaking to be part of your studies, and I'm not just talking about discussing the topic at hand amongst yourselves in your grammar class.
If you are going to be studying abroad in Germany, unless you are part of a program which specifically registers your in advance for specific courses or a plan of study, you will have to register after you arrive in Germany. When you do so, depending on the university and the timing of your arrival, how you go about this will likely be different than you are used to back home.