Nothing too complicated, really. You just sign up at a local driving school, you attend a set number of theory lessions, a number of "standard" driving practise lessons (e.g. urban/city/country roads), some highway practise lessons and night drive lessons.
Once you finished all theory lessons, you can take your theoretical exam at the Technical Supervisory Association ("Technischer Überwachungsverein", or "TÜV" in German), in which you have to fill out a questionnaire. If you answer a question wrong (or, if there are various "right" options but you don't check all of them), said question will add a certain amount of points (not all questions are "worth" the same amount), and once you reach a set number of points, you failed the test. I don't remember if it were 8 or 10 points, though.
Once you finished all your practise lessons, you can take the practical exam, in which you and your driving instructor will be joined by another instructor from the TÜV. It's pretty much like a normal 45 minute lesson (except for the nervousness of course) in which you do a bit of everything. Funny enough, if you happen to get stuck in traffic for 45 minutes, they also count towards the exam, so it might happen that you leave the TÜV, get stuck on the highway and return to the TÜV one hour later.
If your German is any good, you might want to have a look at
http://de.wikipedia.org/wiki/Fahrausbildung_und_Fahrerlaubnisprüfung as well.
